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

Source	DF	SS	MS	F	P
Group	2	72.00	36.00	0.79	0.481
Error	9	408.00	45.33
Total	11	480.00

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. 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?

If the cart is moving on the positive $x$-axis, the $x$-component of velocity must be positive.

If the cart is moving on the positive x-axis, the x-component of velocity must be negative.

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.

Ecologists believe that organic material decays over time according to an exponential decay model. This is the case 0 < $\beta$ < 1 in the exponential regression model, for which $\mu_y$ decreases over time. The rate of decay is determined by a number of factors, including composition of material, temperature, and humidity. In an experiment carried out by researchers at the University of Georgia Ecology Institute, leaf litter was allowed to sit for a 20-week period in a bag in a moderately forested area. Initially, the total weight of the organic mass in the bag was 75.0 kg. Each week, the remaining amount (y) was measured. The table shows the weighty by x = number of weeks of time that have passed.

The exponential regression model has prediction equation $\hat{y}$ = $80.6{(0.813)}^x$. Find the predicted weight

(i) initially and

(ii) after 20 weeks.