MCQ TESTING OF HYPOTHESIS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "MCQ TESTING OF HYPOTHESIS"

Transcription

1 MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Test-statistic MCQ 13.2 Any hypothesis which is tested for the purpose of rejection under the assumption that it is true is called: (a) Null hypothesis (b) Alternative hypothesis (c) Statistical hypothesis (d) Composite hypothesis MCQ 13.3 A statement about the value of a population parameter is called: (a) Null hypothesis (b) Alternative hypothesis (c) Simple hypothesis (d) Composite hypothesis MCQ 13.4 Any statement whose validity is tested on the basis of a sample is called: (a) Null hypothesis (b) Alternative hypothesis (c) Statistical hypothesis (b) Simple hypothesis MCQ 13.5 A quantitative statement about a population is called: (a) Research hypothesis (b) Composite hypothesis (c) Simple hypothesis (d) Statistical hypothesis MCQ 13.6 A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false is called: (a) Simple hypothesis (b) Composite hypothesis (c) Statistical hypothesis (d) Alternative hypothesis MCQ 13.7 The alternative hypothesis is also called: (a) Null hypothesis (b) Statistical hypothesis (c) Research hypothesis (d) Simple hypothesis MCQ 13.8 A hypothesis that specifies all the values of parameter is called: (a) Simple hypothesis (b) Composite hypothesis (c) Statistical hypothesis (d) None of the above MCQ 13.9 The hypothesis µ 10 is a: (a) Simple hypothesis (b) Composite hypothesis (c) Alternative hypothesis (d) Difficult to tell. MCQ If a hypothesis specifies the population distribution is called: (a) Simple hypothesis (b) Composite hypothesis (c) Alternative hypothesis (d) None of the above MCQ A hypothesis may be classified as: (a) Simple (b) Composite (c) Null (d) All of the above MCQ The probability of rejecting the null hypothesis when it is true is called: (a) Level of confidence (b) Level of significance (c) Power of the test (d) Difficult to tell

2 MCQ The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected is said to be: (a) Critical region (b) Critical value (c) Acceptance region (d) Significant region MCQ If the critical region is located equally in both sides of the sampling distribution of test-statistic, the test is called: (a) One tailed (b) Two tailed (c) Right tailed (d) Left tailed MCQ The choice of one-tailed test and two-tailed test depends upon: (a) Null hypothesis (b) Alternative hypothesis (c) None of these (d) Composite hypotheses MCQ Test of hypothesis Ho: µ = 50 against H 1 : µ > 50 leads to: (a) Left-tailed test (b) Right-tailed test (c) Two-tailed test (d) Difficult to tell MCQ Test of hypothesis Ho: µ = 20 against H 1 : µ < 20 leads to: (a) Right one-sided test (b) Left one-sided test (c) Two-sided test (d) All of the above MCQ Testing Ho: µ = 25 against H 1 : µ 20 leads to: (a) Two-tailed test (b) Left-tailed test (c) Right-tailed test (d) Neither (a), (b) and (c) MCQ A rule or formula that provides a basis for testing a null hypothesis is called: (a) Test-statistic (b) Population statistic (c) Both of these (d) None of the above MCQ The range of test statistic-z is: (a) 0 to 1 (b) -1 to +1 (c) 0 to (d) - to + MCQ The range of test statistic-t is: (a) 0 to (b) 0 to 1 (c) - to + (d) -1 to +1 MCQ If H o is true and we reject it is called: (a) Type-I error (b) Type-II error (c) Standard error (d) Sampling error MCQ The probability associated with committing type-i error is: (a) β (b) α (c) 1 β (d) 1 α MCQ A failing student is passed by an examiner, it is an example of: (a) Type-I error (b) Type-II error (c) Unbiased decision (d) Difficult to tell

3 MCQ A passing student is failed by an examiner, it is an example of: (a) Type-I error (b) Type-II error (c) Best decision (d) All of the above MCQ α is also called: (a) Confidence coefficient (b) Power of the test (c) Size of the test (d) Level of significance MCQ α is the probability associated with: (a) Type-I error (b) Type-II error (c) Level of confidence (d) Level of significance MCQ Area of the rejection region depends on: (a) Size of α (b) Size of β (c) Test-statistic (d) Number of values MCQ Size of critical region is known as: (a) β (b) 1 - β (c) Critical value (d) Size of the test MCQ A null hypothesis is rejected if the value of a test statistic lies in the: (a) Rejection region (b) Acceptance region (c) Both (a) and (b) (d) Neither (a) nor (b) MCQ The test statistic is equal to: MCQ Level of significance is also called: (a) Power of the test (b) Size of the test (c) Level of confidence (d) Confidence coefficient MCQ Level of significance α lies between: (a) -1 and +1 (b) 0 and 1 (c) 0 and n (d) - to + MCQ Critical region is also called: (a) Acceptance region (b) Rejection region (c) Confidence region (d) Statistical region MCQ The probability of rejecting H o when it is false is called: (a) Power of the test (b) Size of the test (c) Level of confidence (d) Confidence coefficient MCQ Power of a test is related to: (a) Type-I error (b) Type-II error (c) Both (a) and (b) (d) Neither (a) and (b)

4 MCQ In testing hypothesis α + β is always equal to: (a) One (b) Zero (c) Two (d) Difficult to tell MCQ The significance level is the risk of: (a) Rejecting H o when H o is correct (c) Rejecting H 1 when H 1 is correct (b) Rejecting H o when H 1 is correct (d) Accepting H o when H o is correct. MCQ An example in a two-sided alternative hypothesis is: (a) H 1 : µ < 0 (b) H 1 : µ > 0 (c) H 1 : µ 0 (d) H 1 : µ 0 MCQ If the magnitude of calculated value of t is less than the tabulated value of t and H 1 is two-sided, we should: (a) Reject H o (b) Accept H 1 (c) Not reject H o (d) Difficult to tell MCQ Accepting a null hypothesis H o : (a) Proves that H o is true (b) Proves that H o is false (c) Implies that H o is likely to be true (d) Proves that µ 0 MCQ The chance of rejecting a true hypothesis decreases when sample size is: (a) Decreased (b) Increased (c) Constant (d) Both (a) and (b) MCQ The equality condition always appears in: (a) Null hypothesis (b) Simple hypothesis (c) Alternative hypothesis (d) Both (a) and (b) MCQ Which hypothesis is always in an inequality form? (a) Null hypothesis (b) Alternative hypothesis (c) Simple hypothesis (d) Composite hypothesis MCQ Which of the following is composite hypothesis? (a) µ µ o (b) µ µ o (c) µ = µ o (d) µ µ o MCQ P (Type I error) is equal to: (a) 1 α (b) 1 β (c) α (d) β MCQ P (Type II error) is equal to: (a) α (b) β (c) 1 α (d) 1 β MCQ The power of the test is equal to: (a) α (b) β (c) 1 α (d) 1 β

5 MCQ The degree of confidence is equal to: (a) α (b) β (c) 1 α (d) 1 β MCQ α / 2 is called: (a) One tailed significance level (c) Left tailed significance level (b) Two tailed significance level (d) Right tailed significance level MCQ Student s t-test is applicable only when: (a) n 30 and σ is known (b) n>30 and σ is unknown (c) n=30 and σ is known (d) All of the above MCQ Student s t-statistic is applicable in case of: (a) Equal number of samples (b) Unequal number of samples (c) Small samples (d) All of the above MCQ Paired t-test is applicable when the observations in the two samples are: (a) Equal in number (b) Paired (c) Correlation (d) All of the above MCQ The degree of freedom for paired t-test based on n pairs of observations is: (a) 2n - 1 (b) n - 2 (c) 2(n - 1) (d) n - 1 MCQ The test-statistic has d.f = : (a) n (b) n - 1 (c) n - 2 (d) n 1 + n 2-2 MCQ In an unpaired samples t-test with sample sizes n 1 = 11 and n 2 = 11, the value of tabulated t should be obtained for: (a) 10 degrees of freedom (b) 21 degrees of freedom (c) 22 degrees of freedom (d) 20 degrees of freedom MCQ In analyzing the results of an experiment involving seven paired samples, tabulated t should be obtained for: (a) 13 degrees of freedom (b) 6 degrees of freedom (c) 12 degrees of freedom (d) 14 degrees of freedom MCQ The mean difference between 16 paired observations is 25 and the standard deviation of differences is 10. The value of statistic-t is: (a) 4 (b) 10 (c) 16 (d) 25 MCQ Statistic-t is defined as deviation of sample mean from population mean µ expressed in terms of: (a) Standard deviation (b) Standard error (c) Coefficient of standard deviation (d) Coefficient of variation

6 MCQ Student s t-distribution has (n-1) d.f. when all the n observations in the sample are: (a) Dependent (b) Independent (c) Maximum (d) Minimum MCQ The number of independent values in a set of values is called: (a) Test-statistic (b) Degree of freedom (c) Level of significance (d) Level of confidence MCQ The purpose of statistical inference is: (a) To collect sample data and use them to formulate hypotheses about a population (b) To draw conclusion about populations and then collect sample data to support the conclusions (c) To draw conclusions about populations from sample data (d) To draw conclusions about the known value of population parameter MCQ Suppose that the null hypothesis is true and it is rejected, is known as: (a) A type-i error, and its probability is β (b) A type-i error, and its probability is α (c) A type-ii error, and its probability is α (d) A type-il error, and its probability is β MCQ An advertising agency wants to test the hypothesis that the proportion of adults in Pakistan who read a Sunday Magazine is 25 percent. The null hypothesis is that the proportion reading the Sunday Magazine is: (a) Different from 25% (b) Equal to 25% (c) Less than 25 % (d) More than 25 % MCQ If the mean of a particular population is µo, is distributed: (a) As a standard normal variable, if the population is non-normal (b) As a standard normal variable, if the sample is large (c) As a standard normal variable, if the population is normal (d) As the t-distribution with v = n - 1 degrees of freedom MCQ If µ 1 and µ 2 are means of two populations, is distributed: (a) As a standard normal variable, if both samples are independent and less than 30 (b) As a standard normal variable, if both populations are normal (c) As both (a) and (b) state (d) As the t-distribution with n 1 + n 2-2 degrees of freedom MCQ If the population proportion equals p o, then is distributed: (a) As a standard normal variable, if n > 30 (b) As a Poisson variable (c) As the t-distribution with v= n 1 degrees of freedom (d) As a distribution with v degrees of freedom

7 MCQ When σ is known, the hypothesis about population mean is tested by: (a) t-test (b) Z-test (c) χ 2 -test (d) F-test MCQ Given µ o = 130, = 150, σ = 25 and n = 4; what test statistics is appropriate? (a) t (b) Z (c) χ 2 (d) F MCQ Given H o : µ = µ o, H 1 : µ µ o, α = 0.05 and we reject H o ; the absolute value of the Z-statistic must have equalled or been beyond what value? (a) 1.96 (b) 1.65 (c) 2.58 (d) 2.33 MCQ If p 1 and p 2 are not identical, then standard error of the difference of proportions (p 1 p 2 ) is: MCQ Under the hypothesis Ho: p 1 = p 2, the formula for the standard error of the difference between proportions (p 1 p 2 ) is:

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

More information

Chapter 7. Section Introduction to Hypothesis Testing

Chapter 7. Section Introduction to Hypothesis Testing Section 7.1 - Introduction to Hypothesis Testing Chapter 7 Objectives: State a null hypothesis and an alternative hypothesis Identify type I and type II errors and interpret the level of significance Determine

More information

Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35

Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen.  John Nerbonne 1/35 Statistiek I t-tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistiek-i/ John Nerbonne 1/35 t-tests To test an average or pair of averages when σ is known, we

More information

Section 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)

Section 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935) Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis

More information

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

More information

Hypothesis testing - Steps

Hypothesis testing - Steps Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =

More information

Hypothesis Testing (unknown σ)

Hypothesis Testing (unknown σ) Hypothesis Testing (unknown σ) Business Statistics Recall: Plan for Today Null and Alternative Hypotheses Types of errors: type I, type II Types of correct decisions: type A, type B Level of Significance

More information

Hypothesis Testing. Bluman Chapter 8

Hypothesis Testing. Bluman Chapter 8 CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 8-1 Steps in Traditional Method 8-2 z Test for a Mean 8-3 t Test for a Mean 8-4 z Test for a Proportion 8-5 2 Test for

More information

Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions

Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions Chapter 12 Hypothesis Testing Learning Objectives Examine the process of hypothesis testing Evaluate research and null hypothesis Determine one- or two-tailed tests Understand obtained values, significance,

More information

Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses

Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the

More information

General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine

More information

Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Introduction to Hypothesis Testing Chapter 8 Student Lecture Notes 8-1 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate

More information

Chapter 9. Section Correlation

Chapter 9. Section Correlation Chapter 9 Section 9.1 - Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation

More information

Confidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%)

Confidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%) Confidence Interval A confidence interval (or interval estimate) is a range (or an interval) of values used to estimate the true value of a population parameter. A confidence interval is sometimes abbreviated

More information

Chapter Additional: Standard Deviation and Chi- Square

Chapter Additional: Standard Deviation and Chi- Square Chapter Additional: Standard Deviation and Chi- Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret

More information

PASS Sample Size Software

PASS Sample Size Software Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

More information

Hypothesis Testing --- One Mean

Hypothesis Testing --- One Mean Hypothesis Testing --- One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis

More information

Practice Exam. 1. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35

Practice Exam. 1. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35 Practice Exam Use the following to answer questions 1-2: A census is done in a given region. Following are the populations of the towns in that particular region (in thousands): 35, 46, 52, 63, 64, 71,

More information

Stat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015

Stat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015 Stat 411/511 THE RANDOMIZATION TEST Oct 16 2015 Charlotte Wickham stat511.cwick.co.nz Today Review randomization model Conduct randomization test What about CIs? Using a t-distribution as an approximation

More information

Pearson's Correlation Tests

Pearson's Correlation Tests Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation

More information

HYPOTHESIS TESTING: POWER OF THE TEST

HYPOTHESIS TESTING: POWER OF THE TEST HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,

More information

t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon

t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com

More information

Two-Sample T-Tests Assuming Equal Variance (Enter Means)

Two-Sample T-Tests Assuming Equal Variance (Enter Means) Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of

More information

THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.

THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7. THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM

More information

Module 5 Hypotheses Tests: Comparing Two Groups

Module 5 Hypotheses Tests: Comparing Two Groups Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this

More information

Factorial Analysis of Variance

Factorial Analysis of Variance Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

More information

Hypothesis Testing I

Hypothesis Testing I ypothesis Testing I The testing process:. Assumption about population(s) parameter(s) is made, called null hypothesis, denoted. 2. Then the alternative is chosen (often just a negation of the null hypothesis),

More information

Multiple Hypothesis Testing: The F-test

Multiple Hypothesis Testing: The F-test Multiple Hypothesis Testing: The F-test Matt Blackwell December 3, 2008 1 A bit of review When moving into the matrix version of linear regression, it is easy to lose sight of the big picture and get lost

More information

Structure of the Data. Paired Samples. Overview. The data from a paired design can be tabulated in this form. Individual Y 1 Y 2 d i = Y 1 Y

Structure of the Data. Paired Samples. Overview. The data from a paired design can be tabulated in this form. Individual Y 1 Y 2 d i = Y 1 Y Structure of the Data Paired Samples Bret Larget Departments of Botany and of Statistics University of Wisconsin Madison Statistics 371 11th November 2005 The data from a paired design can be tabulated

More information

3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples 3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

More information

Chapter 11-12 1 Review

Chapter 11-12 1 Review Chapter 11-12 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data

More information

Inferential Statistics

Inferential Statistics Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

More information

Chapter III. Testing Hypotheses

Chapter III. Testing Hypotheses Chapter III Testing Hypotheses R (Introduction) A statistical hypothesis is an assumption about a population parameter This assumption may or may not be true The best way to determine whether a statistical

More information

Chapter 8. Hypothesis Testing

Chapter 8. Hypothesis Testing Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing

More information

9-3.4 Likelihood ratio test. Neyman-Pearson lemma

9-3.4 Likelihood ratio test. Neyman-Pearson lemma 9-3.4 Likelihood ratio test Neyman-Pearson lemma 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental

More information

7 Hypothesis testing - one sample tests

7 Hypothesis testing - one sample tests 7 Hypothesis testing - one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X

More information

Chapter 9, Part A Hypothesis Tests. Learning objectives

Chapter 9, Part A Hypothesis Tests. Learning objectives Chapter 9, Part A Hypothesis Tests Slide 1 Learning objectives 1. Understand how to develop Null and Alternative Hypotheses 2. Understand Type I and Type II Errors 3. Able to do hypothesis test about population

More information

Testing a claim about a population mean

Testing a claim about a population mean Introductory Statistics Lectures Testing a claim about a population mean One sample hypothesis test of the mean Department of Mathematics Pima Community College Redistribution of this material is prohibited

More information

Statistical Inference and t-tests

Statistical Inference and t-tests 1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

More information

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

More information

Two-Sample T-Tests Allowing Unequal Variance (Enter Difference)

Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption

More information

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing

More information

Point Biserial Correlation Tests

Point Biserial Correlation Tests Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable

More information

Measuring the Power of a Test

Measuring the Power of a Test Textbook Reference: Chapter 9.5 Measuring the Power of a Test An economic problem motivates the statement of a null and alternative hypothesis. For a numeric data set, a decision rule can lead to the rejection

More information

Example Hypotheses. Chapter 8-2: Basics of Hypothesis Testing. A newspaper headline makes the claim: Most workers get their jobs through networking

Example Hypotheses. Chapter 8-2: Basics of Hypothesis Testing. A newspaper headline makes the claim: Most workers get their jobs through networking Chapter 8-2: Basics of Hypothesis Testing Two main activities in statistical inference are using sample data to: 1. estimate a population parameter forming confidence intervals 2. test a hypothesis or

More information

Chapter 14: 1-6, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution?

Chapter 14: 1-6, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution? Chapter 14: 1-6, 9, 1; Chapter 15: 8 Solutions 14-1 When is it appropriate to use the normal approximation to the binomial distribution? The usual recommendation is that the approximation is good if np

More information

8-2 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis

8-2 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis 8-2 Basics of Hypothesis Testing Definitions This section presents individual components of a hypothesis test. We should know and understand the following: How to identify the null hypothesis and alternative

More information

NCSS Statistical Software

NCSS Statistical Software Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

More information

Null Hypothesis H 0. The null hypothesis (denoted by H 0

Null Hypothesis H 0. The null hypothesis (denoted by H 0 Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property

More information

Non-Inferiority Tests for One Mean

Non-Inferiority Tests for One Mean Chapter 45 Non-Inferiority ests for One Mean Introduction his module computes power and sample size for non-inferiority tests in one-sample designs in which the outcome is distributed as a normal random

More information

Power and Sample Size Determination

Power and Sample Size Determination Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,

More information

Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics

Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public

More information

Inferences About Differences Between Means Edpsy 580

Inferences About Differences Between Means Edpsy 580 Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Inferences About Differences Between Means Slide

More information

Null Hypothesis Significance Testing Signifcance Level, Power, t-tests Spring 2014 Jeremy Orloff and Jonathan Bloom

Null Hypothesis Significance Testing Signifcance Level, Power, t-tests Spring 2014 Jeremy Orloff and Jonathan Bloom Null Hypothesis Significance Testing Signifcance Level, Power, t-tests 18.05 Spring 2014 Jeremy Orloff and Jonathan Bloom Simple and composite hypotheses Simple hypothesis: the sampling distribution is

More information

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

More information

Lesson 1: Comparison of Population Means Part c: Comparison of Two- Means

Lesson 1: Comparison of Population Means Part c: Comparison of Two- Means Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis

More information

Simple Linear Regression Inference

Simple Linear Regression Inference Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

More information

Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test)

Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test) Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test) A hypothesis test is conducted when trying to find out if a claim is true or not. And if the claim is true, is it significant.

More information

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

NCSS Statistical Software. One-Sample T-Test

NCSS Statistical Software. One-Sample T-Test Chapter 205 Introduction This procedure provides several reports for making inference about a population mean based on a single sample. These reports include confidence intervals of the mean or median,

More information

Using Excel for inferential statistics

Using Excel for inferential statistics FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied

More information

Guide to Microsoft Excel for calculations, statistics, and plotting data

Guide to Microsoft Excel for calculations, statistics, and plotting data Page 1/47 Guide to Microsoft Excel for calculations, statistics, and plotting data Topic Page A. Writing equations and text 2 1. Writing equations with mathematical operations 2 2. Writing equations with

More information

Statistics Review PSY379

Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

More information

Hypothesis Testing Summary

Hypothesis Testing Summary Hypothesis Testing Summary Hypothesis testing begins with the drawing of a sample and calculating its characteristics (aka, statistics ). A statistical test (a specific form of a hypothesis test) is an

More information

Chapter 5: Basic Statistics and Hypothesis Testing

Chapter 5: Basic Statistics and Hypothesis Testing Chapter 5: Basic Statistics and Hypothesis Testing In this chapter: 1. Viewing the t-value from an OLS regression (UE 5.2.1) 2. Calculating critical t-values and applying the decision rule (UE 5.2.2) 3.

More information

Hypothesis Testing. Hypothesis Testing

Hypothesis Testing. Hypothesis Testing Hypothesis Testing Daniel A. Menascé Department of Computer Science George Mason University 1 Hypothesis Testing Purpose: make inferences about a population parameter by analyzing differences between observed

More information

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

More information

Nonparametric Statistics

Nonparametric Statistics 1 14.1 Using the Binomial Table Nonparametric Statistics In this chapter, we will survey several methods of inference from Nonparametric Statistics. These methods will introduce us to several new tables

More information

Chapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means

Chapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Statistical Inference

Statistical Inference Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

More information

Quantitative Biology Lecture 5 (Hypothesis Testing)

Quantitative Biology Lecture 5 (Hypothesis Testing) 15 th Oct 2015 Quantitative Biology Lecture 5 (Hypothesis Testing) Gurinder Singh Mickey Atwal Center for Quantitative Biology Summary Classification Errors Statistical significance T-tests Q-values (Traditional)

More information

Sampling and Hypothesis Testing

Sampling and Hypothesis Testing Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters

More information

How to Conduct a Hypothesis Test

How to Conduct a Hypothesis Test How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some

More information

AP STATISTICS 2009 SCORING GUIDELINES (Form B)

AP STATISTICS 2009 SCORING GUIDELINES (Form B) AP STATISTICS 2009 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) state the appropriate hypotheses, (2) identify and

More information

3. Nonparametric methods

3. Nonparametric methods 3. Nonparametric methods If the probability distributions of the statistical variables are unknown or are not as required (e.g. normality assumption violated), then we may still apply nonparametric tests

More information

Principles of Hypothesis Testing for Public Health

Principles of Hypothesis Testing for Public Health Principles of Hypothesis Testing for Public Health Laura Lee Johnson, Ph.D. Statistician National Center for Complementary and Alternative Medicine johnslau@mail.nih.gov Fall 2011 Answers to Questions

More information

HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Class: Date: HypoTesting Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A Type II error is committed if we make: a. a correct decision when the

More information

Power and Sample Size. In epigenetic epidemiology studies

Power and Sample Size. In epigenetic epidemiology studies Power and Sample Size In epigenetic epidemiology studies Overview Pros and cons Working examples Concerns for epigenetic epidemiology Definition Power is the probability of detecting an effect, given that

More information

CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

More information

Hypothesis Testing or How to Decide to Decide Edpsy 580

Hypothesis Testing or How to Decide to Decide Edpsy 580 Hypothesis Testing or How to Decide to Decide Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Hypothesis Testing or How to Decide to Decide

More information

22. HYPOTHESIS TESTING

22. HYPOTHESIS TESTING 22. HYPOTHESIS TESTING Often, we need to make decisions based on incomplete information. Do the data support some belief ( hypothesis ) about the value of a population parameter? Is OJ Simpson guilty?

More information

6: Introduction to Hypothesis Testing

6: Introduction to Hypothesis Testing 6: Introduction to Hypothesis Testing Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance

More information

HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR

HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR Hypothesis is a conjecture (an inferring) about one or more population parameters. Null Hypothesis (H 0 ) is a statement of no difference or no relationship

More information

Study Guide for the Final Exam

Study Guide for the Final Exam Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

More information

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More information

Nonparametric Methods for Two Samples. Nonparametric Methods for Two Samples

Nonparametric Methods for Two Samples. Nonparametric Methods for Two Samples Nonparametric Methods for Two Samples An overview In the independent two-sample t-test, we assume normality, independence, and equal variances. This t-test is robust against nonnormality, but is sensitive

More information

Paired 2 Sample t-test

Paired 2 Sample t-test Variations of the t-test: Paired 2 Sample 1 Paired 2 Sample t-test Suppose we are interested in the effect of different sampling strategies on the quality of data we recover from archaeological field surveys.

More information

Regression Analysis: A Complete Example

Regression Analysis: A Complete Example Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

More information

Statistical Functions in Excel

Statistical Functions in Excel Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.

More information

Hypothesis Testing and Confidence Interval Estimation

Hypothesis Testing and Confidence Interval Estimation Biostatistics for Health Care Researchers: A Short Course Hypothesis Testing and Confidence Interval Estimation Presented ed by: Susan M. Perkins, Ph.D. Division of Biostatistics Indiana University School

More information

Probability of rejecting the null hypothesis when

Probability of rejecting the null hypothesis when Sample Size The first question faced by a statistical consultant, and frequently the last, is, How many subjects (animals, units) do I need? This usually results in exploring the size of the treatment

More information

Probability and Statistics Lecture 9: 1 and 2-Sample Estimation

Probability and Statistics Lecture 9: 1 and 2-Sample Estimation Probability and Statistics Lecture 9: 1 and -Sample Estimation to accompany Probability and Statistics for Engineers and Scientists Fatih Cavdur Introduction A statistic θ is said to be an unbiased estimator

More information

Hypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test...

Hypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test... Hypothesis Testing COMP 45 STATISTICS Dr N A Heard Contents 1 Hypothesis Testing 1.1 Introduction........................................ 1. Error Rates and Power of a Test.............................

More information

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.

More information

Data Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments - Introduction

Data Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments - Introduction Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments - Introduction

More information