Look back at 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.

Why are the margins of error larger than with the separate 95% intervals?

Two examples 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 $n_1$ = $n_2$ = $n_3$ = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013.

The confidence intervals are wide. In the design of this experiment, what could you change to estimate the differences in means more precisely?

Two examples 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 $n_1$ = $n_2$ = $n_3$ = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013.

The 95% confidence intervals are (0.3, 9.7) for $\mu_3$ - $\mu_1$ and (-2 .1, 7.3) for $\mu_1$ - $\mu2$. Interpret these two confidence intervals. Using these two intervals and the interval from part a, summarize what the airline company learn ed from this study.

Two examples 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 $n_1$ = $n_2$ = $n_3$ = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013.

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.

Two examples 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 $n_1$ = $n_2$ = $n_3$ = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013.

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.

Do freshmen spent significantly more time on Facebook than other class ranks? A recent study (R. Junco, Journal of Applied Developmental Psychology, 2015, vol. 36, p. 18- 29) investigated the amount of time per day freshman, sophomores, juniors, and seniors spent on Facebook while doing schoolwork. The students surveyed were U.S. residents from a 4-year, public, primarily residential institution in the Northeastern United States. The data from the survey are available on the book 's website, with time measured in minutes. The following table shows the mean time each cohort spent on Facebook and an ANOVA table. Construct a 95% confidence interval to compare the population mean time spent per day on Facebook between freshmen and seniors.

For the House Selling Prices GI) OR data file on the book 's website, the table shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category (New = 0 to 24 years old, Medium = 25 to 50 years old, Old = 51 to 74 years old, Very Old = 75 + years old). It also shows a summary table of means and standard deviations of the selling prices, by age group.

Interpret the confidence interval.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

State and check the assumptions for the test in part b.

For the House Selling Prices GI) OR data file on the book 's website, the table shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category (New = 0 to 24 years old, Medium = 25 to 50 years old, Old = 51 to 74 years old, Very Old = 75 + years old). It also shows a summary table of means and standard deviations of the selling prices, by age group.

Using information given in the tables, show how to construct a 95% confidence interval comparing the population means of new and medium-aged houses.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

For the one-way ANOVA comparing the three mean weight changes, report the test statistic and P-value. Explain how to interpret.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

Construct box plots for the three groups. Use these and sample summary means and standard deviations to describe the three samples.

Use the estimate $\left|R_{N}\right| \leq b_{N+1}$ to find a value of N that guarantees that the sum of the first N terms of the alternating series

$$\sum_{n=1}^{\infty}(-1)^{n+1} b_{n}$$

differs from the infinite sum by at most the given error. Calculate the partial sum $S_N$ for this N. [T] $b_{n}=1 / \sqrt{n}, \quad \text { error }<10^{-3}$

Most of the sentences in the following paragraph contain an error in pronoun usage. Identify each error, and then give the correct pronoun form. If a sentence is already correct, write $C$.

Jim Henson's gifts to all of we puppet fans were some of the most beloved characters in show business-Kermit the Frog, Miss Piggy, and the Cookie Monster, to name a few.

Use the estimate $\left|R_{N}\right| \leq b_{N+1}$ to find a value of N that guarantees that the sum of the first N terms of the alternating series

$$\sum_{n=1}^{\infty}(-1)^{n+1} b_{n}$$

differs from the infinite sum by at most the given error. Calculate the partial sum $S_N$ for this N. [T] $b_{n}=1 / n^{2}, \quad \text { error }<10^{-6}$