The CEO of a company that owns five resort hotels wants to evaluate and compare satisfaction with the five hotels. The company's research department randomly sampled 125 people who had stayed at any of the hotels during the past month and asked them to rate their expectations of the hotel before their stay and to rate the quality of the actual stay at the hotel. Both observations used a rating scale of 0-10, with 0 = very poor and 10 = excellent. The researchers compared the hotels on the gap between prior expectation and actual quality, using the difference score, y = performance gap = (prior expectation score - actual quality score).

State the null and alternative hypotheses for conducting an ANOVA.

A psychologist compares the mean amount of time of rapid-eye movement (REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample means for the three groups were 18, 15, and 12. The table shows the ANOVA table from SPSS.

REM sleep

Would the n1argin of error for each separate 95% confidence interval be less than 13.3, equal to 13.3, or larger than 13.3? Explain why.

Look back at the previous exercise.

Set up indicator variables for a regression model so that an F test for the regression parameters is equivalent to the ANOVA test comparing the three means.

A psychologist compares the mean amount of time of rapid-eye movement (REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample means for the three groups were 18, 15, and 12. The table shows the ANOVA table from SPSS.

REM sleep

For the Tukey 95% multiple comparison confidence intervals comparing each pair of means, the margin of error for each interval is 13.3. Is it true or false that since all the confidence intervals contain 0, it is plausible that all three population means equal 0.

A psychologist compares the mean amount of time of rapid-eye movenent ( REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample means for the three groups were 18, 15, and 12. The table shows the ANOVA table from SPSS.

REM sleep

Report and interpret the P-value for the ANOVA F test.

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?

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.

According to this method, which groups are significantly different?

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.

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.

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.