# STAT 3090 Test 3 - Version A Fall 2015

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Multiple Choice: (Questions 1-16) Answer the following questions on the scantron provided using a #2 pencil. Bubble the response that best answers the question. Each multiple choice correct response is worth 3 points. For your record, also circle your choice on your exam since the scantron will not be returned to you. Only the responses recorded on your scantron will be graded. 1. A wildlife study is designed to find the mean weight of salmon caught by an Alaskan fishing company. A preliminary study of a random sample of 50 salmon showed a sample standard deviation of 2.15 pounds. How large a sample should be taken to be 95% confident that the sample mean is within 0.2 pound of the true mean weight? A) At least 22 B) At least 30 C) At least 313 D) At least A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.9 months. The conditions for performing a hypothesis test were checked and verified. What is the test statistic in order to test the claim that the new typhoid shot has a smaller variance of protection times than the original? A) χχ 2 = B) χχ 2 = C) χχ 2 = D) χχ 2 = The manufacturer of a dietary shake claims their shakes will help people lose weight. The company obtains a random sample of 300 adults over the age of 25 who take the shake once a day as a replacement of one meal. The participants mean weight loss after 4 weeks was found to be 0.76 pound with standard deviation weight loss of 3.4 pounds. If you wanted to determine if there was sufficient evidence that the dietary shake performs as the company claims, which of the following are the appropriate hypotheses for this test? A) HH 0 : μμ = 0.76 HH AA : μμ < 0.76 B) HH 0 : pp = 0.76 HH AA : pp < 0.76 C) HH 0 : μμ = 0 HH AA : μμ > 0 D) HH 0 : pp = 0.76 HH AA : pp > 0.76 Page 1 of 11

2 4. A random sample of 20 adult coyotes in a region of northern Minnesota showed the average age to be 2.05 years, with a sample standard deviation of 0.82 years. However, it is thought that the overall population mean age of coyotes is You would like to test if the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years. The conditions for performing a hypothesis test were checked and verified. What is the appropriate rejection region for this hypothesis test at the 0.05 significance level? A) t > 1.73 B) t > 1.96 C) z > 1.96 D) t > Some boxes of a certain brand of cereal include a voucher for a free Redbox video rental inside the box. The company that makes the cereal claims that a voucher can be found in 20 percent of the boxes. However, based on their experiences eating this cereal at home, a group of students believes that the proportion of boxes with vouchers is less than 0.2. This group of students purchased 65 boxes of cereal to investigate the company s claim. Below is the Minitab output of the appropriate hypothesis test. Test and CI for One Proportion Test of p = 0.2 vs p < 0.2 Sample X N Sample p 95% Upper Bound Z-Value P-Value Using the normal approximation. Which of the following is the correct interpretation of the p-value of this test? A) The sample proportion differs from the population proportion by B) The sample proportion is standard deviations above the mean. C) If the population proportion is 0.2, the probability of obtaining a test statistic of or less is D) The probability that the population proportion is 0.02 is The mayor of a town believes that 54% of the residents favor annexation of an adjoining community. A random sample of 1000 voters from the town showed that 51% of the residents favored annexation. What is the population of interest for a test to determine if there is sufficient evidence at the 0.01 level to refute the mayor's claim? A. All 1000 voters B. 510 residents that favored annexation C. All voters in this town D. All voters in the town that favor annexation Page 2 of 11

3 7. Each individual in a random sample of 60 college students was asked how much money he or she spent on food in a typical month. The data was then used to construct a 99% confidence interval for the actual mean amount spent on food for all students at the college in a typical month. The confidence interval was (\$240, \$380). Which of the following is true about this 99% confidence interval for a population mean? A) The population mean falls exactly in the middle of the interval B) There is a 1% probability that the interval \$240 to \$380 will not capture the population mean C) The sample mean falls exactly in the middle of the interval D) All of the individuals sampled spent between \$240 and \$380 in a typical month. 8. A pharmaceutical company has developed a new drug to reduce cholesterol. The company collected data by giving the new drug to a random sample of 50 people from the population of people with high cholesterol. The reduction in cholesterol level after one month of use was recorded for each individual in the sample, resulting in a sample mean reduction and standard deviation of 24 mg/dl and 15 mg/dl respectively. A 99% confidence interval for the population mean reduction in cholesterol level for the new drug is found to be (19.737, ). Interpret what it means to be 99% confident in this interval. A) There is a 99% probability that the population mean reduction in cholesterol level for the new drug is contained in the interval to B) In repeated sampling, using the same method used to create the interval to , 99% of the intervals created will capture the population mean reduction in cholesterol level for the new drug. C) In repeated sampling, 99% of the sample means calculated will fall in the interval to D) There is a 99% chance that the interval to will capture the mean reduction in cholesterol level for the new drug of the 50 people sampled. 9. Which of the following are the conditions for inference for a chi-square test for standard deviation? I. Random Sample from the population II. χχ 2 is normally distributed III. Population random variable is normally distributed IV. Sample size is larger than 30 A) I and II B) I and III C) I and IV D) I and III or IV Page 3 of 11

4 10. In a marketing survey, a random sample of 1001 supermarket shoppers revealed that 273 always stock up on an item when they find that item at a real bargain price. What is the critical value for a 97% confidence interval for the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain? A) 1.88 B) 2.17 C) 0.52 D) The manufacturer of processed deli meats reports that the standard deviation of the number of carbohydrates in its smoke turkey breast is 0.5 gram per 2 ounce serving. A dietician does not believe the manufacturer and random selects eighteen 2 ounce servings of the smoked turkey breast and determines the number of carbohydrates per serving. The standard deviation of the number of carbs is computed to be 0.62 gram per serving. The conditions for performing a hypothesis test were checked and verified. If you are performing a hypothesis test to determine if there is sufficient evidence to indicate that the standard deviation is not 0.5 gram per serving at the 0.05 level of significance what is the appropriate rejection region? A) χχ 2 < oooo χχ 2 > B) χχ 2 < oooo χχ 2 > C) χχ 2 > D) χχ 2 < oooo χχ 2 > A Harris Interactive poll conducted during January 2008 found that 944 of 1748 randomly selected adult Americans 18 years or older who do not have a tattoo believe that individuals with tattoos are more rebellious. Obtain a point estimate for the proportion of Americans without tattoos who believe individuals with tattoos are more rebellious A) 944 B) 0.54 C) D) What is the relationship between α (probability of Type 1 error) and β (probability of type 2 error)? A) As α increases, β increases B) As α increases, β decreases C) The relationship depends on the context of the hypothesis test D) Both α and β are independent of one another Page 4 of 11

5 14. Which of the following is certain to reduce the width of a confidence level? A) Larger sample size and higher confidence level B) Larger sample size and lower confidence level C) Smaller sample size and higher confidence level D) Smaller sample size and lower confidence level 15. A consumer group wishes to test Apple's claim that the ipad has a 10-hour battery life. After running a random sample of 15 ipads under identical conditions, the group finds a 99% confidence interval for the mean battery life of an ipad to be (8.45, 10.05) hours. Assuming battery life of an ipad is approximately normally distributed, does this confidence interval provide evidence that the ipad does not have an average battery life of 10 hours? A) No, because the 99% confidence interval contains 10 hours. B) Yes, because 10 is near the upper endpoint of the confidence interval and the majority of the plausible values for the mean battery life of an ipad are less than 10 hours. C) Yes, because if a 95% confidence interval for the true mean battery life were constructed it most likely would not contain 10 hours. D) The sample size is not large enough to make a conclusion about the mean battery life of an ipad. 16. A humane society wanted to estimate with 95 percent confidence the proportion of households in its county that own at least one dog. The humane society selected a random sample of households in its county and used the sample to estimate the proportion of all households that own at least one dog. The conditions for calculating a 95 percent confidence interval for the proportion of households in this county that own at least one dog were checked and verified, and the resulting confidence interval is in the Minitab output below. What is the margin of error for the interval calculated? Test and CI for One Proportion Sample X N Sample p 95% CI ( , ) Using the normal approximation. A) B) C) D) Page 5 of 11

6 Free Response: The Free Response questions will count 52% of your total grade. Read each question carefully. In order to receive full credit you must show legible and logical (relevant) justification which supports your final answer. You MUST show your work. Answers with no justification will receive no credit. 1. (4 pts) A magazine company is planning to survey customers to determine the proportion who will renew their subscription for the coming year. The magazine wants to estimate the population proportion with 95% confidence and a margin of error equal to What is the minimum sample size required? Show work by filling in values to the appropriate formula and give units. 1 points correct z-value 1 point for following formula 1 point for rounding up 1 point units -0.5 for minor arithmetic errors nn = (1.96)2 (0.5) = nn = 1068 cccccccccccccccccc Page 6 of 11

7 2. Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. Assume tip income is normally distributed. The data are given in the table below: \$2.25 \$2.50 \$2.25 \$2.00 \$2.00 \$1.50 \$1.25 \$2.00 \$1.50 \$2.00 \$3.00 \$1.50 The sample standard deviation of the data above is Suppose the owner is interested in developing a 90% confidence interval for the population mean tip income per delivery. A) (4pts) List and verify the conditions required to calculate the appropriate confidence interval. 1. Randomly sample from population stated in problem 2. XX normally distributed population normally distributed is stated in the problem therefore x-bar is normally distributed 1 point for each condition, 1 point for each justification Grading Notes: It is ok if student states random sample as condition, however just random is not ok Must indicate that random sample is stated in the problem either by stating or underlying random in problem some indication that this condition was checked correctly (not just a check mark) B) (5 pts) Calculate the appropriate 90% confidence interval. Show work by filling in values to the appropriate formula and giving calculations to 3 decimal places. ss XX ± tt αα 2 nn ± (1.796) (1.723, 2.235) 1 point for correct point estimate (1.979) (notation xx and value) 2 points for correct critical value (notation t and value) 2 points for correct standard error notation and value Grading Notes: Must show formula and values plugged into formula Subtract 1 for minor calculation errors Intervals with no formula (or only computer syntax) will receive NO credit Page 7 of 11

8 C) (6 pts) Interpret the interval you found in part b. We are 90% confident that the interval to captures the population mean tip income per delivery. If clearly stating interpretation about sample proportion mark entire part as incorrect. Otherwise o 2 points for using the word confidence (not probability, likely, chance, etc.) sure is ok o 2 points for the correct context of the problem o 2 points for clearly stating population mean ( population, all, true etc.) Page 8 of 11

9 3. A report summarized a survey of 304 randomly selected US businesses. Of these companies, 238 indicated that they monitor employees web site visits. Is there sufficient evidence to suggest that more than 75% of US businesses monitor employees web site visits? Test the appropriate hypotheses using a significance level of 0.01 and the step below. a. (4 pts) Give the appropriate hypotheses for this test. HH 0 : pp = 0.75 HH AA : pp > 0.75 Where pp is the population proportion of companies that monitor employees web site visits. (not necessary to receive full credit) [1 point for population symbol, 1 point for proportion, 1 point for signs, 1 point for value] (if used x-bar minus 2) b. (4 pts) List and Verify conditions for the appropriate hypothesis test 1. Randomly sample from population stated in problem 2. P-hat normally distributed nnnn = 304(0.75) = 228 5; nn(1 pp) = 304(0.25) = point for each condition, 1 point for each justification Grading Notes: It is ok if student states random sample as condition, however just random is not ok Must indicate that random sample is stated in the problem either by stating or underlying random in problem some indication that this condition was checked correctly (not just a check mark) It is ok if student states nnnn 5; nn(1 pp) 5 as the condition rather than p-hat normally distributed. In other words the statement nnnn = 304(0.75) = 228 5; nn(1 pp) = 304(0.25) = 76 5 will receive credit for condition and justification Must indicate some comparison to 5 (cannot just calculate 228 and 76 without indicating comparing them to 5) If the student uses hats when stating the condition they lose the point for the condition but may get credit for checking condition. If an extra condition is stated and checked (such as population normally distributed) subtract 1 point c. (3 pts) Give the appropriate test statistic. Show formula, work, and value. zz = pp pp pp(1 pp) nn = (0.75)(0.25) 304 = 1.21 [-1 for minor arithmetic errors, -3 for reversing p-hat and p, -1 for formula without values plugged in] Page 9 of 11

10 d. (5 pts) Find the appropriate p-value. Draw an appropriate picture, show work, and give the value to 4 decimal places. P(Z > 1.21) = pt for work (picture or formula or probability statement), 2pts for p-value, 2 pts for picture - find rejection region -3 for p-value and work) - incorrect rejection region -4 e. (5 pts) What is your decision regarding the null hypothesis? Explain. At the 1% significance level, my p-value (0.1131) is greater than alpha (0.01) therefore I do not reject the null hypothesis. - Correct decision with no reason why -3 - Correct decision with Wrong or invalid comparison -3 - Incorrect decision with valid comparison -3 f. (5 pts) What are your conclusions about this particular test? There is insufficient evidence to suggest the population proportion of US businesses that monitor employee s webs site visits is greater than 75%. - Conclusion correct decision but NOT about alternative hypothesis -2 - no indication of population parameter (US, population, etc.) -1 - with correct conclusion but not in context -1 - with correct conclusion but not about proportion/percentage -1 - If conclusion is clearly about sample proportion -5 - If conclusion is not consistent with decision from part e (indicating wrong conclusion) -5 Page 10 of 11

11 4. (6 pts) When a law firm represents a group of people in a class action lawsuit and wins that lawsuit, the firm receives a percentage of the group s monetary settlement. That settlement amount is based on the total number of people in the group the larger the group and the larger the settlement, the more money the firm will receive. A law firm is trying to decide whether to represent car owners in a class action lawsuit against the manufacturer of a certain make and model for a particular defect. If 5 percent or less of the cars of this make and model have the defect, the firm will not recover its expenses. Therefore, the firm will handle the lawsuit only if it is convinced that more than 5 percent of cars of this make and model have the defect. The firm plans to take a random sample of 1,000 people who bought this car and ask them if they experienced this defect in their cars. The lawyers are testing the following hypothesis: HH 0 : pp = 0.05 HH AA : pp > 0.05 a. In the context of this situation, describe a Type II error. Type II error would be finding that the proportion of cars of this make and model have the defect when is not greater than 0.05 when in fact it is greater than 5%. 3 pts - Either right or wrong b. Describe a consequence of that error for the law firm. The law firm will not pursue lawsuit when it would potentially be profitable for them. 3 pts A logical consequence based on their answer in part a. 5. (1 pt) If your scantron is correctly bubbled with a #2 pencil, with your correct XID (with the C bubbled in as a 0 ), your correct test version, AND the front of your test is completed with your signature on the academic integrity statement, you earn 1 point. END OF TEST Page 11 of 11

### Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

### 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

### Name: (b) Find the minimum sample size you should use in order for your estimate to be within 0.03 of p when the confidence level is 95%.

Chapter 7-8 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. Please indicate which program

### p ˆ (sample mean and sample

Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics

### 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

### Homework 5 Solutions

Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces

### AP Statistics 2011 Scoring Guidelines

AP Statistics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

### 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

### CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING MULTIPLE CHOICE 56. In testing the hypotheses H 0 : µ = 50 vs. H 1 : µ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized

### Section 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities

Today: Section 2.2, Lesson 3: What can go wrong with hypothesis testing Section 2.4: Hypothesis tests for difference in two proportions ANNOUNCEMENTS: No discussion today. Check your grades on eee and

### AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

### A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777

Math 210 - Exam 4 - Sample Exam 1) What is the p-value for testing H1: µ < 90 if the test statistic is t=-1.592 and n=8? A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 2) The owner of a football team claims that

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

Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

### 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

### FINAL EXAM REVIEW - Fa 13

FINAL EXAM REVIEW - Fa 13 Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. 1) The temperatures of eight different plastic spheres. 2) The sample

### 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

### 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,

### Prob & Stats. Chapter 9 Review

Chapter 9 Review Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally

### p1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0.

Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested

### AP Statistics 2010 Scoring Guidelines

AP Statistics 2010 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

### 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

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

Sample Final Exam Spring 2008 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given degree of confidence and sample data to construct

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

STATISTICS/GRACEY EXAM 3 PRACTICE/CH. 8-9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the P-value for the indicated hypothesis test. 1) A

### Extending Hypothesis Testing. p-values & confidence intervals

Extending Hypothesis Testing p-values & confidence intervals So far: how to state a question in the form of two hypotheses (null and alternative), how to assess the data, how to answer the question by

### 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.............................

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

STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.

### 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

### Margin of Error When Estimating a Population Proportion

Margin of Error When Estimating a Population Proportion Student Outcomes Students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in

### AP Statistics 2001 Solutions and Scoring Guidelines

AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use

### 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

### Construct a scatterplot for the given data. 2) x Answer:

Review for Test 5 STA 2023 spr 2014 Name Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents

### Stats Review Chapters 9-10

Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

### Math 251, Review Questions for Test 3 Rough Answers

Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

### Mind on Statistics. Chapter 10

Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine

### 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

### 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

### 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

### Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

### 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

### BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

### Lesson 17: Margin of Error When Estimating a Population Proportion

Margin of Error When Estimating a Population Proportion Classwork In this lesson, you will find and interpret the standard deviation of a simulated distribution for a sample proportion and use this information

### 8 6 X 2 Test for a Variance or Standard Deviation

Section 8 6 x 2 Test for a Variance or Standard Deviation 437 This test uses the P-value method. Therefore, it is not necessary to enter a significance level. 1. Select MegaStat>Hypothesis Tests>Proportion

### 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

### Lesson 2: Calculating Probabilities of Events Using Two-Way Tables

Calculating Probabilities of Events Using Two-Way Tables Classwork Example 1: Building a New High School The school board of Waldo, a rural town in the Midwest, is considering building a new high school

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

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

### 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

### Chapter Five: Paired Samples Methods 1/38

Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery

### Hypothesis testing for µ:

University of California, Los Angeles Department of Statistics Statistics 13 Elements of a hypothesis test: Hypothesis testing Instructor: Nicolas Christou 1. Null hypothesis, H 0 (always =). 2. Alternative

### 9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis. 1) Which could be the null hypothesis for the true proportion

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

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### AP Statistics 2012 Scoring Guidelines

AP Statistics 2012 Scoring Guidelines The College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the

### Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

### MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6

MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/6 "Pepsi" problem A market research consultant hired by the Pepsi-Cola Co. is interested

### 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

### 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

### Chapter 8: Introduction to Hypothesis Testing

Chapter 8: Introduction to Hypothesis Testing We re now at the point where we can discuss the logic of hypothesis testing. This procedure will underlie the statistical analyses that we ll use for the remainder

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

Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide

### 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

### 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

### Lecture 13 More on hypothesis testing

Lecture 13 More on hypothesis testing Thais Paiva STA 111 - Summer 2013 Term II July 22, 2013 1 / 27 Thais Paiva STA 111 - Summer 2013 Term II Lecture 13, 07/22/2013 Lecture Plan 1 Type I and type II error

### 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

### 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

### 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

### 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

### Hypothesis. Testing Examples and Case Studies. Chapter 23. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc.

Hypothesis Chapter 23 Testing Examples and Case Studies Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc. 23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis

### 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

### 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

### 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

### Name: Date: D) 3141 3168

Name: Date: 1. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for

### Hints for Success on the AP Statistics Exam. (Compiled by Zack Bigner)

Hints for Success on the AP Statistics Exam. (Compiled by Zack Bigner) The Exam The AP Stat exam has 2 sections that take 90 minutes each. The first section is 40 multiple choice questions, and the second

### 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

### MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample

MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of

### 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 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

### Review. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results

MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population

### Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative

### AP Statistics 2005 Scoring Guidelines

AP Statistics 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college

### SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

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

Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between

### 1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700

Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,

### Step 1: Set up hypotheses that ask a question about the population by setting up two opposite statements about the possible value of the parameters.

HYPOTHESIS TEST CLASS NOTES Hypothesis Test: Procedure that allows us to ask a question about an unknown population parameter Uses sample data to draw a conclusion about the unknown population parameter.

### 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

### 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

### Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.

Practice problems for Homework 1 - confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the

### Point and Interval Estimates

Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number

### Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:

Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

### 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,

### 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 =

### AP Statistics 2009 Scoring Guidelines Form B

AP Statistics 2009 Scoring Guidelines Form B The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded

### Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB

Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB DIRECTIONS: Welcome! Your TA will help you apply your Calculator and MINITAB to review Business Stats, and will

### Chapter 7 - Practice Problems 1

Chapter 7 - Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the

### Sample Exam #1 Elementary Statistics

Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables

### Math 140 (4,5,6) Sample Exam II Fall 2011

Math 140 (4,5,6) Sample Exam II Fall 2011 Provide an appropriate response. 1) In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies,

### AP STATISTICS 2010 SCORING GUIDELINES

2010 SCORING GUIDELINES Question 4 Intent of Question The primary goals of this question were to (1) assess students ability to calculate an expected value and a standard deviation; (2) recognize the applicability

### Results from the 2014 AP Statistics Exam. Jessica Utts, University of California, Irvine Chief Reader, AP Statistics jutts@uci.edu

Results from the 2014 AP Statistics Exam Jessica Utts, University of California, Irvine Chief Reader, AP Statistics jutts@uci.edu The six free-response questions Question #1: Extracurricular activities

### CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHI-SQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chi-square tests of independence we use the hypotheses. H0: The variables are independent

### Chapter 23 Inferences About Means

Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute