17. Push-ups. Every year the students at Gossett High

1. More eggs? Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They plan to run their experiment for a month, recording the number of eggs each hen produces. a) Design an experiment that will require a two-sample t procedure to analyze the results. b) Design an experiment that will require a matchedpairs t procedure to analyze the results. c) Which experiment would you consider the stronger design? Why?

2. MTV. Some students do homework with the TV on. (Anyone come to mind?) Some researchers want to see if people can work as effectively with as without distraction. The researchers will time some volunteers to see how long it takes them to complete some relatively easy crossword puzzles. During some of the trials, the room will be quiet; during other trials in the same room, a TV will be on, tuned to MTV. a) Design an experiment that will require a two-sample t procedure to analyze the results. b) Design an experiment that will require a matchedpairs t procedure to analyze the results. c) Which experiment would you consider the stronger design? Why?

3. Sex sells? Ads for many products use sexual images to try to attract attention to the product. But do these ads bring peoples attention to the item that was being advertised? We want to design an experiment to see if the presence of sexual images in an advertisement affects peoples ability to remember the product. a) Describe an experimental design requiring a matchedpairs t procedure to analyze the results. b) Describe an experimental design requiring an independent sample procedure to analyze the results.

4. Freshman 15? Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true. a) Describe a study design that would require a matched-pairs t procedure to analyze the results. b) Describe a study design that would require a twosample t procedure to analyze the results.

5. Women. Values for the labor force participation rate of women (LFPR) are published by the U.S. Bureau of Labor Statistics. We are interested in whether there was a difference between female participation in 1968 and 1972, a time of rapid change for women. We check LFPR values for 19 randomly selected cities for 1968 and 1972 a) Which of these tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion.

6. Rain. Simpson, Alsen, and Eden (Technometrics 1975) report the results of trials in which clouds were seeded and the amount of rainfall recorded. The authors report on 26 seeded and 26 unseeded clouds in order of the amount of rainfall, largest amount first. Here are two possible tests to study the question of whether cloud seeding works. Which test is appropriate for these data? Explain your choice. Using the test you select, state your conclusion. a) Which of these tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion.

7. Friday the 13th, I. In 1993 the British Medical Journal published an article titled, Is Friday the 13th Bad for Your Health? Researchers in Britain examined how Friday the 13th affects human behavior. One question waswhether people tend to stay at home more on Friday the 13th. The data below are the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6th and 13th) for five different periods. a) Which of the tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion. c) Are the assumptions and conditions for inference met?

8. Friday the 13th, II: The researchers in Exercise 7 also examined the number of people admitted to emergency rooms for vehicular accidents on 12 Friday evenings (6 each on the 6th and 13th).Based on these data, is there evidence that more people are admitted, on average, on Friday the 13th? Here are two possible analyses of the data: a) Which of these tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion. c) Are the assumptions and conditions for inference met?

9. Online insurance I. After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.) for 10 of his clients and checked online price quotes for their policies. The comparisons are shown in the table below. His statistical software produced the following summaries (where PriceDiff = Local Online): At first, the insurance agent wondered whether there was some kind of mistake in this output. He thought the Pythagorean Theorem of Statistics should work for finding the standard deviation of the price differences in other words, that

10. Windy, part I. To select the site for an electricitygenerating wind turbine, wind speeds were recorded at several potential sites every 6 hours for a year. Two sites not far from each other looked good. Each had a mean wind speed high enough to qualify, but we should choose the site with a higher average daily wind speed. Because the sites are near each other and the wind speeds were recorded at the same times, we should view the speeds as paired. Here are the summaries of the speeds (in miles per hour): Is there a mistake in this output? Why doesnt the Pythagorean Theorem of Statistics work here? In other words, shouldnt

11. Online insurance II. In Exercise 9, we saw summary statistics for 10 drivers car insurance premiums quoted by a local agent and an online company. Here are displays for each companys quotes and for the difference (Local Online): a) Which of the summaries would help you decide whether the online company offers cheaper insurance? Why? b) The standard deviation of PriceDiff is quite a bit smaller than the standard deviation of prices quoted by either the local or online companies. Discuss why. c) Using the information you have, discuss the assumptions and conditions for inference with these data.

12. Windy, part II. In Exercise 10, we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricity-generating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind speed high enough to qualify, but how can we tell which site is best? Here are some displays:a) The boxplots show outliers for each site, yet the histogram shows none. Discuss why. b) Which of the summaries would you use to select between these sites? Why? c) Using the information you have, discuss the assumptions and conditions for paired t inference for these data. (Hint: Think hard about the independence assumption in particular.)

13. Online insurance 3. Exercises 9 and 11 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.

14. Windy, part III. Exercises 10 and 12 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed.

15. Temperatures. The table below gives the average high temperatures in January and July for several European cities. Write a 90% confidence interval for the mean temperature difference between summer and winter in Europe. Be sure to check conditions for inference, and clearly explain what your interval means.

16. Marathons 2006. The table on the next page shows the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2006. Assuming that performances in the Big Apple resemble performances elsewhere, we can think of these data as a sample of performance in marathon competitions. Create a 90% confidence interval for the mean difference in winning times for male and female marathon competitors. (www.nycmarathon.org)

17. Push-ups. Every year the students at Gossett High School take a physical fitness test during their gym classes. One component of the test asks them to do as many push-ups as they can. Results for one class are shown below, separately for boys and girls. Assuming that students at Gossett are assigned to gym classes at random, create a 90% confidence interval for how many more push-ups boys can do than girls, on average, at that high school.

18. Brain waves. An experiment was performed to see whether sensory deprivation over an extended period of time has any effect on the alpha-wave patterns produced by the brain. To determine this, 20 subjects, inmates in a Canadian prison, were randomly split into two groups. Members of one group were placed in solitary confinement. Those in the other group were allowed to remain in their own cells. Seven days later, alpha-wave frequencies were measured for all subjects, as shown in the following table. (P. Gendreau et al., "Changes in EEG Alpha Frequency and Evoked Response Latency During Solitary Confinement," Journal of Abnormal Psychology 79 [1972]: 54-59) a) What are the null and alternative hypotheses? Be sure to define all the terms and symbols you use. b) Are the assumptions necessary for inference met? c) Perform the appropriate test, indicating the formula you used, the calculated value of the test statistic, the df, and the P-value. d) State your conclusion.

19. Job satisfaction. (When you first read about this exercise break plan in Chapter 24, you did not have an inference method that would work. Try again now.) A company institutes an exercise break for its workers to see if it will improve job satisfaction, as measured by a questionnaire that assesses workers satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below. a) Identify the procedure you would use to assess the effectiveness of the exercise program, and check to see if the conditions allow the use of that procedure. b) Test an appropriate hypothesis and state your conclusion. c) If your conclusion turns out to be incorrect, what kind of error did you commit?

20. Summer school. (When you first read about the summer school issue in Chapter 24 you did not have an inference method that would work. Try again now.) Having done poorly on their Math final exams in June, six students repeat the course in summer school and take another exam in August. a) If we consider these students to be representative of all students who might attend this summer school in other years, do these results provide evidence that the program is worthwhile? b) This conclusion, of course, may be incorrect. If so, which type of error was made?

21. Yogurt. Is there a significant difference in calories between servings of strawberry and vanilla yogurt? Based on the data shown in the table, test an appropriatehypothesis and state your conclusion. Dont forget to check assumptions and conditions!

22. Gasoline. Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decided by a coin toss, and the mileage for that tankful is recorded. Then the mileage is recorded again for the same cars for a tankful of the other kind of gasoline. We dont let the drivers know about this experiment. Here are the results (miles per gallon): a) Is there evidence that cars get significantly better fuel economy with premium gasoline? b) How big might that difference be? Check a 90% confidence interval. c) Even if the difference is significant, why might the company choose to stick with regular gasoline? d) Suppose you had done a bad thing. (Were sure you didnt.) Suppose you had mistakenly treated these data as two independent samples instead of matched pairs. What would the significance test have found? Carefully explain why the results are so different.

23. Braking test. A tire manufacturer tested the braking performance of one of its tire models on a test track. The company tried the tires on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table. a) Write a 95% confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means. b) Write a 95% confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.

24. Braking test 2. For another test of the tires in Exercise 23, a car made repeated stops from 60 miles per hour. The test was run on both dry and wet pavement, with results as shown in the table. (Note that actual braking distance, which takes into account the drivers reaction time, is much longer, typically nearly 300 feet at 60 mph!) a) Write a 95% confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means. b) Write a 95% confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.

25. Tuition 2006. How much more do public colleges and universities charge out-of-state students for tuition per semester? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data. Tuition figures per semester are rounded to the nearest hundred dollars. a) Create a 90% confidence interval for the mean difference in cost. Be sure to justify your procedure. b) Interpret your interval in context. c) A national magazine claims that public institutions charge state residents an average of $3500 less than out-of-staters for tuition each semester. What does your confidence interval indicate about this assertion?

26. Sex sells, part II. In Exercise 3 you considered the question of whether sexual images in ads affected peoples abilities to remember the item being advertised. To investigate, a group of Statistics students cut ads out of magazines. They were careful to find two ads for each of 10 similar items, one with a sexual image and one without. They arranged the ads in random order and had 39 subjects look at them for one minute. Then they asked the subjects to list as many of the products as they could remember. Their data are shown in the table. Is there evidence that the sexual images mattered?

27. Strikes. Advertisements for an instructional video claim that the techniques will improve the ability of Little League pitchers to throw strikes and that, after undergoing the training, players will be able to throw strikes on at least 60% of their pitches. To test this claim, we have 20 Little Leaguers throw 50 pitches each, and we record the number of strikes. After the players participate in the training program, we repeat the test. The table shows the number of strikes each player threw before and after the training. a) Is there evidence that after training players can throw strikes more than 60% of the time? b) Is there evidence that the training is effective in improving a players ability to throw strikes?

28. Freshman 15, revisited. In Exercise 4 you thought about how to design a study to see if its true that students tend to gain weight during their first year in college. Well, Cornell Professor of Nutrition David Levitsky did just that. He recruited students from two large sections of an introductory health course. Although they were volunteers, they appeared to match the rest of the freshman class in terms of demographic variables such as sex and ethnicity. The students were weighed during the first week of the semester, then again 12 weeks later. Based on Professor Levitskys data, estimate the mean weight gain in first-semester freshmen and comment on the freshman 15. (Weights are in pounds.)