An airline has a toll-free telephone number for reservations. Often the call volume is heavy, and callers are placed on hold until a reservation agent is free to answer. The airline hopes a caller remains on hold until the call is answered, so as not to lose a potential customer. The airline recently conducted a randomized experiment to analyze whether callers would remain on hold longer, on average, if they heard (a) an advertisement about the airline and its current promotions, (b) Muzak, or (c) classical music (Vivaldi's Four Seasons). The company randomly selected one out of every 1000 calls in a particular week. For each call, they randomly selected one of the three recordings to play and then measured the number of minutes that the caller remained on hold before hanging up (these calls were purposely not answered). The sample means were 5.4,2.8, and 10.4, with n1 = n2 = n3 = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013. a) A 95% confidence interval comparing the population mean times that callers are willing to remain on hold for classical music and Muzak is (2.9, 12.3). Interpret this interval. b) The-margin-of error-was 4.7-for-this-comparison. Withont-doing a enleulation, explain-why the-margin of error is 4.7 for eomparing each pair of means: c) The 95% confidence intervals are (0.3,9.7) for µ3 – H1 and (–2.1,7.3) for µ1 – #2. Interpret these two confidence intervals. Using these two intervals and the interval from part a, summarize what the airline company learned from this study. d) The confidence intervals are wide. In the design of this experiment, what could you change to estimate the differences in means more precisely?

Many fundraisers ask for donations using email and text messages. A paper describes an experiment to investigate whether the proportion of people who make a donation when asked for a donation by email is different from the proportion of people who make a donation when asked for a donation in a text message. In this experiment, 1.7% of those who received and opened an email request for a donation and 7.8% of those who received a text message asking for a donation actually made a donation. Assume that the people who received these requests were randomly assigned to one of the two groups (email or text message) and suppose that the given percentages are based on sample sizes of 2,000 (the actual sample sizes in the experiment were much larger). (Let p1 be the proportion who make a donation after receiving an email, and p2 be the proportion who make a donation after receiving a text message.) Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to two…

For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of  167  houses built in Southern California between 1950 and 1985 and an independent, random sample of  80  houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained  71  houses with pools, and the sample of houses built from 1992-present contained  31  houses with pools. Based on this survey, can we conclude, at the  0.05  level of significance, that the proportion  p1  of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion  p2  of all Southern California houses built from…

The authors of a research article were interested in the effect on female viewers of watching movies in which female heroines were portrayed in roles that focus on their sex appeal. They carried out an experiment in which female college students were assigned at random to one of two experimental groups. The 24 women in one group watched 13 minutes of scenes from a certain superhero film series and then responded to a questionnaire designed to measure body esteem. Lower scores on this measure correspond to lower body satisfaction. The 29 women in the other group (the control group) did not watch any video prior to responding to the questionnaire measuring body esteem. For the women who watched the video, the mean body esteem score was 4.44 and the standard deviation was 1.02. For the women in the control group, the mean body esteem score was 5.07 and the standard deviation was 0.96. For purposes of this exercise, you may assume that the distribution of body esteem scores for each of the…