Look back at the previous exercise.

The prediction equation from fitting the multiple regression model equals $\hat{y}$ = 12 + 6$x_1$ + 3$x_2$. Use this equation to find the predicted population means for each group.

These facts have been established at a crime scene: (i) If Professor Plum is not guilty, then the crime took place in the kitchen. (ii) If the crime took place at midni ght, then Professor Plum is guilty. (iii) Miss Scarlet is innocent if and on ly if the weapon was not the candlestick. (iv) Either the weapon was the candlestick or the crime took place in the library. (v) Either Miss Scarlet or Professor Plum is guilty. Use each of the following as a sixth clue to solve the case. Explain your answer. (a) The crime took place in the library. (b) The crime did not take place in the library . (c) The crime was committed at noon with the revolver. (d) The crime took place at midnight in the conservatory. (Give a complete answer.)

Look back at the previous exercise.

Express the null hypothesis both in terms of population means and in terms of regression parameters for the model in part a.

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

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.

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.