Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from0 to 200 and follow (approximately) a Normal distribution with mean 113 and standard deviation 16. You suspect that incoming freshmen at your school have a mean m thatis different from 113 because they are often excited yet anxious about entering college. You give the SSHA to 23 incoming freshmen and find their mean score to be116.7. Conduct a test of significance using a level of significance of a = 0.05.

State the conclusion of the significance test in context.

A. We fail to reject the null hypothesis and conclude that there is not enough significant evidence to conclude that the mean SSHA score among all incoming freshman isdifferent from the national average.

B. We fail to reject the null hypothesis and conclude that there is significant evidence to conclude that the mean SSHA score among all incoming freshman is differentfrom the national average.

C. We reject the null hypothesis and conclude that there is significant evidence to conclude that the mean SSHA score among all incoming freshman is different from thenational average.

D.We reject the null hypothesis and conclude that there is not enough significant evidence to conclude that the mean SSHA score among all incoming freshman isdifferent from the national average.

Answer 1

: A. We fail to reject the null hypothesis and conclude that there is not enough significant evidence to conclude that the mean SSHA score among allincoming freshman is different from the national average.

Answer 2

The test statistic is
t=(xbar-m)/(s/vn)
=(116.7-113)/(16/sqrt(23))
=1.109036

Given a=0.05, |t(0.025, df=n-1=22)|=2.07 (check student t table)
Since 1.109036 is less than 2.07, we do not reject Ho.