Question

1. The provost at the University of Chicago claimed that the entering class this year is larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The University’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Round final answers to two decimal places. Solutions only.

(A) The parameter the president is interested in is:
(a) the mean number of entering students to his university this year.
(b) the mean number of entering students to all U.S. universities this year.
(c) the mean SAT score of the entering students to his university this year.
(d) the mean SAT score of the entering students to all U.S. universities this year.

(e) None of the above.

(B) The population the president is interested in is:
(a) all entering students to all universities in the U.S this year.

(b) all entering students to his university this year.
(c) all SAT test centers in the U.S. this year.
(d) the SAT scores of all students entering universities in the U.S. this year.

(e) None of the above.

(F) True, False, or Uncertain: The null hypothesis would be rejected.

(G) True, False, or Uncertain: The null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

(I) True, False, or Uncertain: The evidence proves beyond a doubt that the mean SAT score of the entering class this year is lower than previous years.

(J) True, False, or Uncertain: If these data were used to perform a two-tail test, the p-value would be 0.1254.

Answer 1

1.

(A)

The correct option is (c).

The parameter the president is interested in is:

(c) the mean SAT score of the entering students to his university this year.

(B)

The correct option is (b).

The population the president is interested in is:

(b) all entering students to his university this year.

(F)

False.

We failed to reject the null hypothesis at 0.05 significance level because p-value of 0.06 is greater than the significance level of 0.05

[decision rule: reject the null hypothesis if p-value is less than the significance level and you will fail to reject it if p-value is greater than or equal to the significance level].

Also, test statistic (-1.60) didn't fall in the rejection region for null hypothesis and thus, we failed to reject the null hypothesis.

(G)

True.

We would reject the null hypothesis at 0.10 significance level as the p-value of 0.06 is less than the significance level of 0.10

Also, the test statistic value of -1.60 fell in the rejection region of null hypothesis.

(I)

False.

At 10% significance level, it can be said that the mean SAT score of the entering class this year is lower than that of previous year's(since, we rejected H0) but at 5% significance level, it cannot be said that the mean SAT score of the entering class this year is lower than that of previous year's (since, we failed to reject H0).

And even at 10% significance level, the given statement is not true because the statement says-"beyond doubt" and there is a doubt of 10% that it is not lower than that of previous year's mean SAT score.

(J)

True.

At 5% significance level, for two-tailed test, for the calculated test statistic value of -1.603, the p-value would be 0.1254.