Question

For the following, indicate whether you should use a one sample t-test, paired t-test, or two sample t-test and whether you have chosen a one-sided or two-sided alternate hypothesis:

A) Do macroeconomics students at Vanderbilt score significantly higher on the Math SAT than the national average?

My Answer: One sample t-test, one tailed

B) Do macroeconomics students at Vanderbilt score significantly higher on the Verbal SAT than the national average?

My answer: One sample t-test, one tailed

C) Report a 95 percent confidence interval for the true mean Math SAT score. Do 95 percent of students have Math SAT scores that fall within this interval? Explain your answer.

My answer: One sample t-test, one tailed

D) Is there a statistically significant difference between the Verbal and Math scores of macroeconomics students at Vanderbilt?

My Answer: Paired t-test, two tailed

E) Is there a statistically significant difference between the performances of males and females on the Verbal SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My Answer: Two sample t-test, two tailed

F) Is there a statistically significant difference between the performances of males and females on the Math SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed

G) Is there a statistically significant difference between the freshman GPAs of males and females? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed

Could someone please double check my answers and if any are incorrect, explain to me where I went wrong? Thanks!

Answer 1

A) Do macroeconomics students at Vanderbilt score significantly higher on the Math SAT than the national average?

My Answer: One sample t-test, one tailed (Correct)

B) Do macroeconomics students at Vanderbilt score significantly higher on the Verbal SAT than the national average?

My answer: One sample t-test, one tailed (Correct)

C) Report a 95 percent confidence interval for the true mean Math SAT score. Do 95 percent of students have Math SAT scores that fall within this interval? Explain your answer.

D) Is there a statistically significant difference between the Verbal and Math scores of macroeconomics students at Vanderbilt?

My Answer: Paired t-test, two tailed (Correct)

E) Is there a statistically significant difference between the performances of males and females on the Verbal SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My Answer: Two sample t-test, two tailed. (add: if there is a statistically significant difference between the performances of males and females on the Verbal SAT then 95% C.I. does not contain zero. Otherwise it contains zero.)

F) Is there a statistically significant difference between the performances of males and females on the Math SAT? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed (add: if there is a statistically significant difference between the performances of males and females on the Math SAT then 95% C.I. does not contain zero. Otherwise it contains zero.)

G) Is there a statistically significant difference between the freshman GPAs of males and females? Construct a 95 percent confidence interval for the difference. Does it include zero? Relate this to the conclusion of your test.

My answer: Two sample t-test, two tailed (add: if there is a statistically significant difference between the freshman GPAs of males and females then 95% C.I. does not contain zero. Otherwise it contains zero.)