# STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section:

Size: px
Start display at page:

Download "STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4"

Transcription

1 STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: Make sure you have 8 pages. You will be provided with a table as well, as a separate page. You may use four pages of notes (both sides) and a calculator. Multiple choice questions: There are 32 questions worth 2 points each (32 x 2 pts each = 64 pts). Instructions will be given when those begin on page 4. Free response questions: Show all work. If you need extra space use the back of the page, but make sure to tell us it s there. Total of 36 points; points for each part of each question are shown. 1. (1 pt each) Read the following quote (adapted from one of the medical journal articles for the last discussion), then provide the requested information. Researchers studied students at high risk of academic failure, and compared students who had participated in a government preschool program with a control group of students who had not. They found that of those who participated in the program, 49.7% finished high school, while for those in the control group only 38.5% completed high school, for a difference of 11.2%. The chance of a difference that extreme or more so in the sample if there is no population difference is.01. Because.01 is less than.05, the researchers concluded that participation in the program would be associated with higher high school completion rates for the population of students similar to the ones in the study. a. The notation for the parameter of interest is: p 1 p 2 b. The notation for the sample statistic is: pˆ ˆ 1 p2 c. The p-value =.01 d. The null value = 0 e. The level of significance =.05 f. The value of the sample statistic = (6 pts total) Write the null and alternative hypotheses for each of the following scenarios. Use symbols where possible instead of writing things out in words. You do not need to define the meaning of the symbols in your hypotheses as long as you use standard notation. a. (4 pts) According to Mendel s basic law of inheritance, under certain conditions the ratio of phenotypes for two traits inherited independently should be 9:3:3:1 (for dominant-dominant, dominant-recessive, recessive-dominant and recessive-recessive). To test whether two specific traits really are inherited independently, a researcher plans to investigate the phenotypes for these two traits for a random sample of 900 people. Null hypothesis: p1 = 9, p =, p3 =, p4 = [Note: In order to have the desired ratio and sum to 1, this is what the probabilities would need to be.] Alternative hypothesis: Not all of the probabilities specified in the null hypothesis are correct.

2 b. (2 pts) Researchers speculate that the average amount of time it takes for young adults to react to drinking caffeine is shorter than the average amount of time it takes for older adults to react to drinking caffeine. To study this question, they plan to recruit volunteers from two age groups and have them drink a highly caffeinated beverage. Group 1 is 18 to 25 years old and Group 2 is 60 to 65 years old. After drinking the beverage the participants will be tested to see how long it takes (in minutes) for them to react to the caffeine. (We will assume the researchers have a test for doing this!) Null hypothesis: µ 1 µ 2 = 0 Alternative hypothesis: µ 1 < µ 2 or µ 1 µ 2 < 0 [Mean reaction time is lower for the young group] 3. (14 pts total) A new drug is being proposed for the treatment of migraine headaches. Unfortunately some users in early tests of the drug have reported mild nausea as a side effect. The FDA will reject the drug if it thinks that more than 15% (i.e. 0.15) of the population would suffer from this side effect. In an experiment to test this side effect, 400 people who suffer from migraine headaches receive the new drug and 80 of them report nausea as a side effect. a. (2 pts)define the parameter of interest, giving appropriate notation and writing a sentence saying what it is. p = proportion of the population of migraine headache sufferers that would have nausea as a side effect if they were to take this drug. b. Carry out the 5 steps of a hypothesis test to determine if the FDA should reject the drug. Step 1 (2 pts) Specify the null and alternative hypotheses: Use notation, not words. H 0 : p =.15 H a : p >.15 Step 2 (4 pts) Compute the test statistic. (Show your work): First, compute 80 pˆ p p ˆ = =.20. Then z = = = = p (1 p0).15(.85) n 400 Step 3 (2 pts) Find the p-value: From Table A.1, the area below 2.80 =.9974, so p-value = = Step 4 (2 pts) Decide whether the result is statistically significant (i.e. make a conclusion about the hypotheses); use α = 0.05: You can either say Reject the null hypothesis or The result is statistically significant. Step 5 (2 pts) Report the conclusion in context: Because the null hypothesis is rejected, we can conclude that more than 15% of the population would experience nausea, and the FDA should reject the drug.

3 4. (6 pts total) A survey of n = 686 college students asked (among other things) how important religion is in the student s life (very important, fairly important, not important), and how many hours they typically study in a week during the regular term. The sample sizes and sample mean study hours were as follows: Importance of religion Sample mean (hours) Sample size Very Fairly Not a. (1 pt each) An analysis of variance table for this situation is as follows. Fill in the missing numbers. Source DF SS MS F P ReligImp Error Total NOTE: MSError is found as = and F is = 9.77 b. (3 pts) Write a sentence stating the conclusion that would be made about importance of religion and mean study hours for the population represented by these students. The p-value is so the null hypothesis is rejected. We can conclude that for the population, the mean study hours for at least one of the 3 religious importance groups differs from the others. 5. (4 pts) Suppose the distribution of red blood cell counts for a healthy population is known to have a mean of 5.0 million cells per microliter (cells/mcl) with a standard deviation of 0.4 million cells/mcl. An epidemiologist is concerned that a certain environmental hazard is lowering the count for people in the region. A random sample of 100 people in the region will be taken and the sample mean computed. If there really is no harmful effect, describe what the sampling distribution of the sample mean will be by giving the approximate shape, the mean and the standard deviation (in units of million cells per microliter). The sampling distribution is approximately normal with mean = 5.0 and standard 0.4 deviation = 100 = 0.04

4 MULTIPLE CHOICE You have Exam Version A. Write this on your Scantron on the SUBJECT line. Fill in and bubble your ID at the top of the Scantron. Circle the best answer on this exam paper and bubble in the Scantron sheet. 1. Which of the following is not a correct way to state a null hypothesis? A. H 0 : p ˆ ˆ 1 p2 = 0 [The symbols are for sample proportions; hypotheses are about populations.] B. H 0 : µ d = 10 C. H 0 : µ 1 µ 2 = 0 D. H 0 : p =.5 2. A test to screen for a serious but curable disease is similar to hypothesis testing, with a null hypothesis of no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario it is better to increase the probability of: A. making a Type 1 error, providing treatment when it is not needed. B. making a Type 1 error, not providing treatment when it is needed. C. making a Type 2 error, providing treatment when it is not needed. D. making a Type 2 error, not providing treatment when it is needed. 3. Which of the following would be a legitimate reason for removing an outlier from a dataset? A. The outlier is the result of natural variability in the measurement of interest. B. The outlier clearly belongs to a different population. C. The outlier is more than two standard deviations from the mean. D. The outlier is the only negative number in the dataset. 4. Which of the following null hypotheses would be tested using a chi-square goodness-of-fit test? A. There is no relationship between frequent cell phone use (yes, no) and brain cancer (yes, no). B. There is no relationship between age and opinion on gun control. C. The probabilities that a family with two children will have 2 boys, 1 boy and 1 girl, and 2 girls are ¼, ½ and ¼, respectively. D. The probability that a randomly selected person age 50 of older has arthritis is Suppose that the mean of the sampling distribution for the difference in two sample proportions is 0. This tells us that: A. The two population proportions are both 0. B. The two population proportions are equal to each other. C. The two sample proportions are both 0. D. The two sample proportions are equal to each other. 6. When a random sample is to be taken from a population and a statistic is to be computed, the statistic can also be thought of as A. A point estimate B. A random variable C. Both of the above D. None of the above

5 7. Past data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from a certain professor is: final exam = 50 + (0.5)(midterm). An interpretation of the slope is: A. A student who scored 0 on the midterm would be predicted to score 50 on the final exam. B. A student who scored 2 points higher than another student on the midterm would be predicted to score 1 point higher than the other student on the final exam. C. A student who scored 100 on the midterm would be predicted to score 100 on the final exam. D. None of the above are an interpretation of the slope. 8. If the role of the explanatory (x) variable and the response (y) variable are switched in a regression and correlation situation, which of the following would stay the same? A. The slope of the regression line. B. The intercept of the regression line. C. The correlation between the two variables. D. None of the above would stay the same. 9. If two events are mutually exclusive and both have probability > 0, then A. They must also be independent. B. They cannot also be independent. C. They must also be complements. D. They cannot also be complements. 10. For a sample of 400 blood pressure values, the mean is 120 and the standard deviation is 10. Assuming a bell-shaped curve, which interval is likely to contain almost all (over 99%) of the blood pressure values in the sample? A. 119 to 121 B. 110 to 130 C. 100 to 140 D. 90 to Based on the National Household Survey on Drug Abuse, the percentage of 17-year olds who ever tried cigarette smoking is 56.2%. The relative risk of ever having tried smoking for a 17-year old versus a 12- year old is 3.6. What is the risk of smoking for a 12-year-old (i.e. what was the percentage of 12-year olds who ever tried smoking)? A. 14.1% B. 15.6% C. 52.6% D. 56.2% 12. In a newspaper article about whether the regular use of Vitamin C reduces the risk of getting a cold, a researcher is quoted as saying that Vitamin C performed better than placebo in an experiment, but the difference was not larger than what could be explained by chance. In statistical terms, the researcher is saying the results are. A. due to non-sampling errors. B. definitely due to chance. C. statistically significant. D. not statistically significant.

6 13. A medical treatment has a success rate of.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured? A..04 B..20 C..36 D Suppose that for X = net amount won or lost in a lottery game, the expected value is E(X) = \$0.50. What is the correct interpretation of this value? A. The most likely outcome of a single play is a net loss of 50 cents. B. A player will have a net loss of 50 cents every single time he or she plays this lottery game. C. Over a large number of plays the average outcome for plays is a net loss of 50 cents. D. A mistake must have been made because it s impossible for an expected value to be negative 15. Pulse rates of adult men are approximately normal with a mean of 70 and a standard deviation of 8. Which choice correctly describes how to find the proportion of men that have a pulse rate greater than 78? A. Find the area to the left of z = 1 under a standard normal curve. B. Find the area between z = 1 and z = 1 under a standard normal curve. C. Find the area to the right of z = 1 under a standard normal curve. D. Find the area to the right of z = 1 under a standard normal curve. 16. Which one of the following probabilities is a "cumulative" probability? A. The probability that there are exactly 4 people with Type O+ blood in a sample of 10 people. B. The probability of exactly 3 heads in 6 flips of a coin. C. The probability that the annual rainfall in a certain city next year will be 18 inches. D. The probability that a randomly selected woman's height is 67 inches or less. 17. Suppose a 95% confidence interval for the proportion of Americans who exercise regularly is 0.29 to Which one of the following statements is FALSE? A. It is reasonable to say that more than 40% of Americans exercise regularly. B. It is reasonable to say that more than 25% of Americans exercise regularly. C. The hypothesis that 33% of Americans exercise regularly cannot be rejected. D. It is reasonable to say that fewer than 40% of Americans exercise regularly. 18. Null and alternative hypotheses can be statements about which of the following? A. population parameters. B. sample estimates. C. sample statistics. D. it depends - sometimes population parameters and sometimes sample statistics. 19. A test of H 0 : µ = 0 versus Ha: µ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of α = Which of the following will be the same for both researchers? A. The p-value of the test. B. The power of the test if the true µ = 6. C. The value of the test statistic. D. The decision about whether or not to reject the null hypothesis.

7 20. Consider a random sample of 100 females and 100 males. Suppose 15 of the females are left-handed and 12 of the males are left-handed. What is the estimated difference between population proportions of females and males who are left-handed (females males)? Select the choice with the correct notation and numerical value. A. p 1 p 2 = 3 B. p 1 p 2 = 0.03 C. pˆ ˆ 1 p2 = 3 D. pˆ ˆ 1 p2 = The confidence level for a confidence interval for a mean is A. the probability of making a Type 1 error if the interval is used to test a null hypothesis about the population mean. B. the probability that individuals in the population have values that fall into the interval. C. the probability that the procedure provides an interval that covers the sample mean. D. the probability that the procedure provides an interval that covers the population mean. 22. A result is called statistically significant whenever A. The null hypothesis is true. B. The alternative hypothesis is true. C. The p-value is less than or equal to the significance level. D. The p-value is larger than the significance level. 23. A test for a disease has sensitivity of 0.9. If 50 people who have the disease are independently tested, the number who have a positive test result will be: A. a binomial random variable. B. 90% of those tested. C. 45 people D. 5 people 24. A random variable cannot be both normal and A. continuous B. uniform C. symmetric D. have mean of Which of the following would NOT be a problem in a sample survey? A. Placebo effect. B. Asking the uninformed. C. Ordering of the questions. D. Unnecessary complexity of the questions. 26. Which of the following is true about the standard deviation of x? A. it increases as n increases B. it decreases as n increases C. it stays the same as n increases D. it is an estimate of the standard error of x

8 27. Which of the following does not have a sampling distribution? A. Sample proportion ˆp B. Sample mean x C. The point estimate for the population proportion D. Population proportion p 28. The mean of the sampling distribution of x1 x2 is: A. always 0 B. always positive C. always negative D. always µ 1 µ The p-value for a one-sided test for a proportion was If the test had been two-sided instead, the p- value would be: A..02 B..04 C..08 D. it depends on whether the one-sided test had a greater than or a less than alternative. 30. The level of significance (usually.05) associated with a significance test is the probability A. that the alternative hypothesis is true. B. that the null hypothesis is true. C. of not rejecting a true null hypothesis. D. of rejecting a true null hypothesis. 31. Analysis of variance is used to test: A. Whether k population variances are all equal. B. Whether k population standard deviations are all equal. C. Whether k population means are all equal. D. Whether k sample means are all equal. 32. A study compared people who routinely drink at least one sugary (i.e. not diet sugar-free) soda a day with people who do not drink soda and found that the relative risk of obesity for the two groups was 2.0, with higher risk for those who drink the soda. From this we can conclude that: A. Drinking sugary soda causes people to be twice as likely to be obese. B. Drinking sugary soda causes people to weigh more than they would otherwise. C. Avoiding drinking sugary soda causes people to lose weight. D. We cannot say anything about how drinking sugary soda affects weight. For use by graders: Page 1: out of 10 Page 2: out of 16 Page 3: out of 10 Free response score: Multiple choice score: Total score:

### STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could

### Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

### Mind on Statistics. Chapter 8

Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

### C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

### Name: Date: Use the following to answer questions 3-4:

Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

### Mind on Statistics. Chapter 4

Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

### Mind on Statistics. Chapter 12

Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

### General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.

General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n

### STAT 350 Practice Final Exam Solution (Spring 2015)

PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

### 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

Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine

### " Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

### 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

### Mind on Statistics. Chapter 13

Mind on Statistics Chapter 13 Sections 13.1-13.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question

### 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

### 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

### Recall this chart that showed how most of our course would be organized:

Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

### 1) The table lists the smoking habits of a group of college students. Answer: 0.218

FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

### a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams?

1. Phone surveys are sometimes used to rate TV shows. Such a survey records several variables listed below. Which ones of them are categorical and which are quantitative? - the number of people watching

### c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

### 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

### Math 425 (Fall 08) Solutions Midterm 2 November 6, 2008

Math 425 (Fall 8) Solutions Midterm 2 November 6, 28 (5 pts) Compute E[X] and Var[X] for i) X a random variable that takes the values, 2, 3 with probabilities.2,.5,.3; ii) X a random variable with the

### BUS/ST 350 Exam 3 Spring 2012

BUS/ST 350 Exam 3 Spring 2012 Name Lab Section ID # INSTRUCTIONS: Write your name, lab section #, and ID# above. Note the statement at the bottom of this page that you must sign when you are finished with

### 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

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

### Unit 27: Comparing Two Means

Unit 27: Comparing Two Means Prerequisites Students should have experience with one-sample t-procedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013

STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean

### August 2012 EXAMINATIONS Solution Part I

August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,

### socscimajor yes no TOTAL female 25 35 60 male 30 27 57 TOTAL 55 62 117

Review for Final Stat 10 (1) The table below shows data for a sample of students from UCLA. (a) What percent of the sampled students are male? 57/117 (b) What proportion of sampled students are social

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### Unit 26: Small Sample Inference for One Mean

Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage

### 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

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### MEASURES OF VARIATION

NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

### Solutions to Homework 6 Statistics 302 Professor Larget

s to Homework 6 Statistics 302 Professor Larget Textbook Exercises 5.29 (Graded for Completeness) What Proportion Have College Degrees? According to the US Census Bureau, about 27.5% of US adults over

### CHAPTER 14 NONPARAMETRIC TESTS

CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences

### Lecture 13. Understanding Probability and Long-Term Expectations

Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).

### Introduction to Hypothesis Testing

I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true

### Review #2. Statistics

Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of

### Name: Date: Use the following to answer questions 2-3:

Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### 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

### 11. Analysis of Case-control Studies Logistic Regression

Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

### Probability and statistical hypothesis testing. Holger Diessel holger.diessel@uni-jena.de

Probability and statistical hypothesis testing Holger Diessel holger.diessel@uni-jena.de Probability Two reasons why probability is important for the analysis of linguistic data: Joint and conditional

### STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science

STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science Mondays 2:10 4:00 (GB 220) and Wednesdays 2:10 4:00 (various) Jeffrey Rosenthal Professor of Statistics, University of Toronto

### Basic Concepts in Research and Data Analysis

Basic Concepts in Research and Data Analysis Introduction: A Common Language for Researchers...2 Steps to Follow When Conducting Research...3 The Research Question... 3 The Hypothesis... 4 Defining the

### In the general population of 0 to 4-year-olds, the annual incidence of asthma is 1.4%

Hypothesis Testing for a Proportion Example: We are interested in the probability of developing asthma over a given one-year period for children 0 to 4 years of age whose mothers smoke in the home In the

### Simple Random Sampling

Source: Frerichs, R.R. Rapid Surveys (unpublished), 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling, but few use this method for

### 1-3 id id no. of respondents 101-300 4 respon 1 responsible for maintenance? 1 = no, 2 = yes, 9 = blank

Basic Data Analysis Graziadio School of Business and Management Data Preparation & Entry Editing: Inspection & Correction Field Edit: Immediate follow-up (complete? legible? comprehensible? consistent?

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

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test

### LAB : THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics

Period Date LAB : THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,

### 3. There are three senior citizens in a room, ages 68, 70, and 72. If a seventy-year-old person enters the room, the

TMTA Statistics Exam 2011 1. Last month, the mean and standard deviation of the paychecks of 10 employees of a small company were \$1250 and \$150, respectively. This month, each one of the 10 employees

### Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

### STT 200 LECTURE 1, SECTION 2,4 RECITATION 7 (10/16/2012)

STT 200 LECTURE 1, SECTION 2,4 RECITATION 7 (10/16/2012) TA: Zhen (Alan) Zhang zhangz19@stt.msu.edu Office hour: (C500 WH) 1:45 2:45PM Tuesday (office tel.: 432-3342) Help-room: (A102 WH) 11:20AM-12:30PM,

### HYPOTHESIS TESTING WITH SPSS:

HYPOTHESIS TESTING WITH SPSS: A NON-STATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER

### Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice

### Mind on Statistics. Chapter 15

Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,

### Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

### Module 2 Probability and Statistics

Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

### Statistics Class Level Test Mu Alpha Theta State 2008

Statistics Class Level Test Mu Alpha Theta State 2008 1. Which of the following are true statements? I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number

Name: OUTLINE SOLUTIONS University of Chicago Graduate School of Business Business 41000: Business Statistics Solution Key Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper

### Adverse Impact Ratio for Females (0/ 1) = 0 (5/ 17) = 0.2941 Adverse impact as defined by the 4/5ths rule was not found in the above data.

1 of 9 12/8/2014 12:57 PM (an On-Line Internet based application) Instructions: Please fill out the information into the form below. Once you have entered your data below, you may select the types of analysis

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### Mind on Statistics. Chapter 2

Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table

### Final Exam Practice Problem Answers

Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

### Find an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.

374 Chapter 8 The Mathematics of Likelihood 8.3 Expected Value Find an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.

### Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010

Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different

### Statistics E100 Fall 2013 Practice Midterm I - A Solutions

STATISTICS E100 FALL 2013 PRACTICE MIDTERM I - A SOLUTIONS PAGE 1 OF 5 Statistics E100 Fall 2013 Practice Midterm I - A Solutions 1. (16 points total) Below is the histogram for the number of medals won

### Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!

Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on

### QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.

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

Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

### 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

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### Categorical Data Analysis

Richard L. Scheaffer University of Florida The reference material and many examples for this section are based on Chapter 8, Analyzing Association Between Categorical Variables, from Statistical Methods

### Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

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

STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

### The power of a test is the of. by using a particular and a. value of the that is an to the value

DEFINITION The power of a test is the of a hypothesis. The of the is by using a particular and a value of the that is an to the value assumed in the. POWER AND THE DESIGN OF EXPERIMENTS Just as is a common

### Lecture 14. Chapter 7: Probability. Rule 1: Rule 2: Rule 3: Nancy Pfenning Stats 1000

Lecture 4 Nancy Pfenning Stats 000 Chapter 7: Probability Last time we established some basic definitions and rules of probability: Rule : P (A C ) = P (A). Rule 2: In general, the probability of one event

### 2 GENETIC DATA ANALYSIS

2.1 Strategies for learning genetics 2 GENETIC DATA ANALYSIS We will begin this lecture by discussing some strategies for learning genetics. Genetics is different from most other biology courses you have

### www.rmsolutions.net R&M Solutons

Ahmed Hassouna, MD Professor of cardiovascular surgery, Ain-Shams University, EGYPT. Diploma of medical statistics and clinical trial, Paris 6 university, Paris. 1A- Choose the best answer The duration

### Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for

### MATH 2200 PROBABILITY AND STATISTICS M2200FL083.1

MATH 2200 PROBABILITY AND STATISTICS M2200FL083.1 In almost all problems, I have given the answers to four significant digits. If your answer is slightly different from one of mine, consider that to be

### ACMS 10140 Section 02 Elements of Statistics October 28, 2010. Midterm Examination II

ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages of the examination

### 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

### AP Stats Chapter 13. Section 13.1: Comparing Two Means. Characteristics of two sample problems: What are the three conditions for comparing two means?

Section 13.1: Comparing Two Means Characteristics of two sample problems: AP Stats Chapter 13 What are the three conditions for comparing two means? When two population means are compared you can do one

### Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this

### Lecture Notes Module 1

Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific

### Practice Problems and Exams

Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 2009-2010

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### PRACTICE PROBLEMS FOR BIOSTATISTICS

PRACTICE PROBLEMS FOR BIOSTATISTICS BIOSTATISTICS DESCRIBING DATA, THE NORMAL DISTRIBUTION 1. The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period.

### SIMON FRASER UNIVERSITY

SIMON FRASER UNIVERSITY BUEC 333: Statistics for Business and Economics. MIDTERM EXAM: PART I Instructor: Alex Jameson Appiah February. 27, 1996. Time: 50 mins. Name: ------------------------------------------------------

### Online 12 - Sections 9.1 and 9.2-Doug Ensley

Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics - Ensley Assignment: Online 12 - Sections 9.1 and 9.2 1. Does a P-value of 0.001 give strong evidence or not especially strong

### ch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

ch12 practice test 1) The null hypothesis that x and y are is H0: = 0. 1) 2) When a two-sided significance test about a population slope has a P-value below 0.05, the 95% confidence interval for A) does

### Hypothesis Testing. Steps for a hypothesis test:

Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption