Chapter 14.2, Problem 15PB

Tukey holding time comparisons Refer to the previous exercise. We could instead use the Tukey method to construct multiple comparison confidence intervals. The Tukey confidence intervals having overall confidence level 95% have margins of error of 5.7, compared to 4.7 for the separate 95% confidence intervals in the previous exercise.

1. a. According to this method, which groups are significantly different?
2. b. Why are the margins of error larger than with the separate 95% intervals?

Comparing telephone holding times Examples 2 and 3 analyzed whether telephone callers to an airline would stay on hold different lengths of time, on average, if they heard (a) an advertisement about the airline, (b) Muzak, or (c) classical music. 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.

1. 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.
2. b. The margin of error was 4.7 for this comparison. Without doing a calculation, explain why the margin of error is 4.7 for comparing each pair of means.
3. c. The 95% confidence intervals are (0.3, 9.7) for µ₃ – µ₁ and (–2.1, 7.3) for µ₁ – µ₂-Interpret these two confidence intervals. Using these two intervals and the interval from part a, summarize what the airline company learned from this study.
4. d. The confidence intervals are wide. In the design of this experiment, what could you change to estimate the differences in means more precisely?