NY Marathon The table below shows the winning times (in minutes) for men and women in

Which method? Which of the following scenarios should be analyzed as paired data? a) Students take a MCAT prep course. Their before and after scores are compared. b) 20 male and 20 females students in class take a midterm. We compare their scores. c) A group of college freshmen are asked about the quality of the university cafeteria. A year later, the same students are asked about the cafeteria again. Do students opinions change during their time at school?

Which method II? Which of the following scenarios should be analyzed as paired data? a) Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives. b) 50 insomnia patients are given a placebo and 50 are given a mild sedative. Which subjects sleep more hours? c) A group of college freshmen and a group of sophomores are asked about the quality of the university cafeteria. Do students opinions change during their time at school?

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 matched-pairs t procedure to analyze the results. c) Which experiment would you consider the stronger design? Why?

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 matched-pairs t procedure to analyze the results. c) Which experiment would you consider the stronger design? Why?

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.

Freshman ? 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 matchedpairs t procedure to analyze the results. b) Describe a study design that would require a twosample t procedure to analyze the results.

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. Shown below is software output for two possible tests: Paired t-Test of m11 - 22 Test Ho: m11972@19682 = 0 vs Ha: m11972 - 19682 _ 0 Mean of Paired Differences = 0.0337 t-Statistic = 2.458 w>18 df p = 0.0244 2-Sample t-Test of m1 - m2 Ho: m1 - m2 = 0 vs Ha: m1 - m2 _ 0 Test Ho: m119722 - m119682 = 0 vs Ha: m119722 - m119682 _ 0 Difference Between Means = 0.0337 t-Statistic = 1.496 w>35 df p = 0.1434 a) Which of these tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion.

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. Paired t-Test of m11 - 22 Mean of Paired Differences = -277.39615 t-Statistic = -3.641 w>25 df p = 0.0012 2-Sample t-Test of m1 - m2 Difference Between Means = -277.4 t-Statistic = -1.998 w>33 df p = 0.0538 a) Which of these tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion.

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 was whether 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. Here are summaries of two possible analyses: Paired t-Test of mu11 - 22 = 0 vs. mu11 - 22 7 0 Mean of Paired Differences: 2022.4 t-Statistic = 2.9377 w>4 df P = 0.0212 2-Sample t-Test of mu1 = mu2 vs. mu1 7 mu2 Difference Between Means: 2022.4 t-Statistic = 0.4273 w>7.998 df P = 0.3402 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?

Friday the 13th, II: The researchers in Exercise 9 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 and on the next page are two possible analyses: Paired t-Test of mu12 - 12 = 0 vs. mu12 - 12 7 0 Mean of Paired Differences = 3.333 t-Statistic = 2.7116 w>5 df P = 0.0211 2-Sample t-Test of mu2 = mu1 vs. mu2 7 mu1 Difference Between Means = 3.333 t-Statistic = 1.6644 w>9.940 df P = 0.0636 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?

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 SD1Local - Online2 = 2SD21Local2 + SD21Online2. But when he checked, he found that 21229.28122 + 1256.26722 = 343.864, not 175.663 as given by the software. Tell him where his mistake is.

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 SD1site2 - site42 = 2SD21site22 + SD21site42? But 213.58622 + 13.42122 = 4.956, not 2.551 as given by the software. Explain why this happened.

Online insurance II In Exercise 11, 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.

Windy, part II In Exercise 12, 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.)

Online insurance Exercises 11 and 13 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.

Windy, part III Exercises 12 and 14 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.

Cars and trucks We have data on the city and highway fuel efficiency of 316 cars and 316 trucks. a) Would it be appropriate to use paired t methods to compare the cars and the trucks? b) Would it be appropriate to use paired t methods to compare the city and highway fuel efficiencies of these vehicles? c) A histogram of the differences (highway city) is shown. Are the conditions for inference satisfied?

Weighing trucks One kind of scale for weighing trucks can measure their weight as they drive across a plate. Is this method consistent with the traditional method of static weighing? Are the conditions for matched pairs inference satisfied? Weights are in 1000s of pounds.

Cars and trucks again In Exercise 17, after deleting an outlying value of -27, the mean difference in fuel efficiencies for the 632 vehicles was 7.37 mpg with a standard deviation of 2.52 mpg. Find a 95% confidence interval for this difference and interpret it in context.

Weighing trucks II Find a 98% confidence interval of the weight differences in Exercise 18. Interpret this interval in context.

Blocking cars and trucks Thinking about the data on fuel efficiency in Exercise 17, why is the blocking accomplished by a matched pairs analysis particularly important for a sample that has both cars and trucks?

Weighing trucks III Consider the weights from Exercise 18. The side-by-side boxplots below show little difference between the two groups. Should this be sufficient to draw a conclusion about the accuracy of the weigh-in-motion scale?

Temperatures The table on the next page 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.

NY Marathon The table below shows the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2011. 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)

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.

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]: 5459) 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.

Job satisfaction (When you first read about this exercise break plan in Chapter 23, 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. 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?

Summer school (When you first read about the summer school issue in Chapter 23 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?

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 appropriate hypothesis and state your conclusion. Dont forget to check assumptions and conditions!

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.

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.

Braking test For another test of the tires in Exercise 31, 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.

Tuition How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data. 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 $7000 less than out-of-staters for tuition each year. What does your confidence interval indicate about this assertion?

Sex sells, part II In Exercise 11 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?

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?

Freshman , revisited In Exercise 6 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.)

Wheelchair marathon The Boston Marathon has had a wheelchair division since 1977. Who do you think is typically faster, the mens marathon winner on foot or the womens wheelchair marathon winner? Because the conditions differ from year to year, and speeds have improved over the years, it seems best to treat these as paired measurements. Here are summary statistics for the pairwise differences in finishing time (in minutes): (www.boston.com/sports/marathon/history/champions/) Summary of wheelchrF - runM N = 34 Mean = -3.57 SD = 35.083 a) Comment on the assumptions and conditions. b) Assuming that these times are representative of such races and the differences appeared acceptable for inference, construct and interpret a 95% confidence interval for the mean difference in finishing times. c) Would a hypothesis test at a = 0.05 reject the null hypothesis of no difference? What conclusion would you draw?

Marathon start-up years When we considered the Boston Marathon in Exercise 37, we were unable to check the Nearly Normal Condition. Heres a histogram of the differences: Those three large differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the start-up years of new events are different; later on, more athletes train and compete. If we omit those three years, the summary statistics change as follows: Summary of wheelchrF - runM N = 31 Mean = -12.794 SD = 18.64 a) Comment on the assumptions and conditions. b) Assuming that these times are representative of such races, construct and interpret a 95% confidence interval for the mean difference in finishing time. c) Would a hypothesis test at a = 0.05 reject the null hypothesis of no difference? What conclusion would you draw?

Color or text? In an experiment, 32 volunteer subjects are briefly shown seven cards, each displaying the name of a color printed in a different color (example: red, blue, and so on). The subject is asked to perform one of two tasks: memorize the order of the words or memorize the order of the colors. Researchers record the number of cards remembered correctly. Then the cards are shuffled and the subject is asked to perform the other task. The table displays the results for each subject. Is there any evidence that either the color or the written word dominates perception? a) What role does randomization play in this experiment? b) Test appropriate hypotheses and state your conclusion.

And it means? Every statement about a confidence interval contains two parts: the level of confidence and the interval. Suppose that an insurance agent estimating the mean loss claimed by clients after home burglaries created the 95% confidence interval ($1644, $2391). a) Whats the margin of error for this estimate? b) Carefully explain what the interval means. c) Carefully explain what the confidence level means.

Batteries We work for the Watchdog for the Consumer consumer advocacy group. Weve been asked to look at a battery company that claims its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries dont last that long, so we decide to test them. To do this, we select 16 batteries and run them until they die. They lasted a mean of 97 hours, with a standard deviation of 12 hours. a) One of the editors of our newsletter (who does not know statistics) says that 97 hours is a lot less than the advertised 100 hours, so we should reject the companys claim. Explain to him the problem with doing that. b) What are the null and alternative hypotheses? c) What assumptions must we make in order to proceed with inference? d) At a 5% level of significance, what do you conclude? e) Suppose that, in fact, the average life of the companys batteries is only 98 hours. Has an error been made in part d? If so, what kind?

Hamsters How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5. a) Create and interpret a 90% confidence interval. b) Would a 98% confidence interval have a larger or smaller margin of error? Explain. c) How many litters must be used to estimate the average litter size to within 1 baby hamster with 95% confidence?

Cramming Students in two basic Spanish classes were required to learn 50 new vocabulary words. One group of 45 students received the list on Monday and studied the words all week. Statistics summarizing this groups scores on Fridays quiz are given. The other group of 25 students did not get the vocabulary list until Thursday. They also took the quiz on Friday, after cramming Thursday night. Then, when they returned to class the following Monday, they were retestedwithout advance warning. Both sets of test scores for these students are shown. a) Did the week-long study group have a mean score significantly higher than that of the overnight crammers? b) Was there a significant difference in the percentages of students who passed the quiz on Friday? c) Is there any evidence that when students cram for a test, their learning does not last for 3 days?