ANOVA, Regression, Chi-square, Hypothesis

1) Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1 Treatment 2 Treatment 3
3 9 6
2 6 3
5 5 5
1 6 5
3 8 5
1 5 4
4 1
7 5
6
4

a. State the null hypothesis and the alternate hypothesis.
b. What is the decision rule?
c. Compute SST, SSE, and SS total.
d. Complete an ANOVA table.
e. State your decision regarding the null hypothesis.
f. If H0 is rejected, can we conclude that treatment 2 and treatment 3 differ? Use the 95 percent level of confidence.

2) There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number of outpatient surgeries performed at each hospital last week. At the .05 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week?

Number of Surgeries Performed
Day St. Luke's St. Vincent Mercy
Monday 14 18 24
Tuesday 20 24 14
Wednesday 16 22 14
Thursday 18 20 22
Friday 20 28 24

3) The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asks the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.

City Police Number of Crimes City Police Number of Crimes
Oxford 15 17 Holgate 17 7
Starksville 17 13 Carey 12 21
Danville 25 5 Whistler 11 19
Athens 27 7 Woodville 22 6

a. If we want to estimate crimes on the basis of the number of police, which variable is the dependent variable and which is the independent variable?
b. Draw a scattered diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of determination.
e. Interpret these statistical measures. Does it surprise you that the relationship is inverse?

4) A sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage (X1), annual income (X2), number of children living (X3), value of assets (X4), status of health in the form of an index (X5), and the average number of social activities per week?such as bowling and dancing (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.0028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6

a. What is the estimated index of satisfaction for a person who first married at 18, has an annual income of $26,500, has three children living, has assets of $156,000, has an index of health status of 141, and has 2.5 social activities a week on the average?
b. Which would add more to satisfaction, an additional income of $10,000 a year or two more social activities a week?

5) A six-sided die is rolled 30 times and the numbers 1 through 6 appear as shown in the following frequency distribution. At the .10 significance level, can we conclude that the die is fair?

Outcome Frequency Outcome Frequency
1 3 4 3
2 6 5 9
3 2 6 7

6) Four brands of light bulbs are being considered for use in the final assembly area of the Saturn plant in Spring Hill, Tennessee. The director of purchasing asked for samples of 100 from each manufacturer. The numbers of acceptable an unacceptable bulbs from each manufacturer are shown below. At the .05 significance level, is there a difference in the quality of the bulbs?

Manufacturer
A B C D
Unacceptable 12 8 5 11
Acceptable 88 92 95 89
Total 100 100 100 100

7) Calorie Watchers has low-calorie breakfasts, lunches, and dinners. IF you join the club, you receive two packaged meals a day. CW claims that you can eat anything you want for the third meal and still lose at least five pounds the first month. Members of the club are weighed before commencing the program and again at the end of the first month. The experiences of a random sample of 11 enrollees are:

Name Weight Change Name Weight Change
Foster Lost Hercher Lost
Taoka Lost Camder Lost
Lange Gained Hinckle Lost
Ruosos Lost Hinkley Lost
Stephens No change Justin Lost
Cantrell Lost

We are interested in whether there has been a weight loss as a result of the Calorie Watchers program.
a. State H0 and H1.
b. Using the .05 level of significance, what is the decision rule?
c. What is your conclusion about the Calorie Watchers program?

8) An industrial psychologist selected a random sample of seven young urban professional couples who owned their homes. The size of their home (square feet) is compared with that of their parents. At the .05 significance level, can we conclude that the yuppies live in larger homes than their parents?

Couple Name Professional Parent Couple Name Professional Parent
Gordon 1,725 1,175 Kuhlman 1,290 1,360
Sharkey 1,310 1,120 Welch 1,880 1,750
Uselding 1,670 1,420 Anderson 1,530 1,440
Bell 1,520 1,640

(See attached file for full problem description)