1) We wish to perform a t-procedure to construct a confidence interval. A stemplot of the data shows major skewness. Roughly how large should the sample size n be for the t-procedure to be reasonably safe to use?
A) No more than 15
B) Less than 15
C) Between 15 and 30
D) If there is skewness in the data, there is no value that is safe to use for n.
E) At least 40
2) In a large northwestern university, an SRS of 100 entering freshmen in 1988 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1990. In 1992 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Letting p1and p2be the proportion of all entering freshmen in 1988 and 1992, who graduated in the bottom third of their high school class?
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 1992 has been reduced, as a result of the tougher admission standards adopted in 1990, compared to the proportion in 1988? To determine this, you test the hypotheses:
H0:p1=p2
HA:p1>p2
What is the p-value of your test?
A) Between 0.10 and 0.05
B) Between 0.01 and 0.001
C) Below 0.001
D) Between 0.05 and 0.01
E) None of the above
3) An SRS of 25 faculty members at a large southeastern university found that 10 felt that the university was supportive of female and minority faculty. An independent SRS of 20 female faculty found that 5 felt that the university was supportive of female and minority faculty. Let p1and p2represent the proportion of all male and female faculty at the university who felt that the university was supportive of female and minority faculty at the time of the survey.
Is there evidence that the proportion of male faculty members was supportive of female and minority faculty is larger than the corresponding proportion for female faculty members? To determine this, you test the hypotheses:
H0:p1=p2
HA:p1>p2
What is the p-value of your test?
A) Between 0.05 and 0.01
B) Larger than 0.05
C) Below 0.001
D) Between 0.005 and 0.001
4) An SRS of 40 San Diego County Schools graduates showed that 26 of the 40 enrolled in a college or university right out of high school.
The proportion for all graduates across the nation who enroll in a college or univeristy right out of high school is 52%. Is there enough evidence at the 5% significance level to suggest that the proportion of San Diego County graduates is greater than the national average? Be sure to include all the parts of the test.