I. Consider the Situation in Which a Sample Is Obtained from A

STAT/EMIS 5377/7377

PRACTICE EXAM I

I. Consider the situation in which a sample is obtained from a

distribution with and . If a random sample of 40

people is selected, what is the probability that is greater than 198?

II. Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Catalyst 1 is currently in use, but since catalyst 2 is cheaper, it will be adopted unless it can be shown that it changes the process yield. A test is run in the pilot plant in which 8 yields are obtained using catalyst 1 resulting in a mean yield of 92.2 with a standard deviation of 2.7. Also, 10 yields are obtained using catalyst 2 resulting in mean yield 93.9 with a standard deviation of 3.1.

(a) State and test appropriate hypotheses for testing whether there is a difference in the mean yields at the level. Carefully state your conclusions. Also, specify the P-value for this test.

(b)Which of the following is not needed in order for the test you used in (a) to be valid?

(choose one)

(i) both populations are normal

(ii) samples are independent
(iii) variances are known
(iv) variances are equal

III. An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course over a specific two week period. The data below indicate the study times and the test scores on an exam given over the material covered during the two weeks.

Study Time Exam

(hours) Score

(X) (Y)

1092

1581

1284

2074

885

1680

1484

2280

(a) Find the equation of the regression line for predicting exam score from number of hours
studied.

(b) Test the hypotheses vs. at the .01 level of significance

(Show all steps, but you do not need to find the P-value.)

(d) For these data calculate SST, SSR, and SSE

IV. Consider the diagram below:

The sum of the squares of the distances indicated by the vertical lines is

(a)SST

(b)SSR

(c)SSE

V. Below is part of the SAS output from PROC REG. The dependent variable is the percentage raise given to employees and the independent variable is a measure of productivity of the employee. As would be expected, there was a positive correlation between the two variables. On the basis of this output, answer the following questions:

(a)To what hypothesis test does the P-value in the table refer? (Just state the null and alternative hypothesis --- do not perform the test.)

(b)What F-value would have been required for the results of the test in (a) to be significant at the .05 level of significance?

(c)Based on this table, what is the estimate of ? (I want a number)

(d)What is Syy? (I want a number)

Analysis of Variance

Sum of Mean

Source DF Squares Square F Value Prob>F

Model 1 31.38553 31.38553 68.707 0.0001

Error 18 8.22247 0.45680

C Total 19 39.60800