Question

A group of 53 college students from a certain liberal arts college were randomly sampled and...

A group of 53 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73. The group of 53 students in the study reported an average of 4.90 drinks per with a standard deviation of 3.74 drinks. Find the p -value for the hypothesis test. The p -value should be rounded to 4-decimal places.

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 4.73

Ha :    4.73

= 4.90

= 4.73

= 3.74

n = 53

Test statistic = z

= ( - ) / / n

= (4.90 - 4.73) / 3.74 / 53

= 0.33

Test statistic = 0.33

P(z > 0.33) = 1 - P(z < 0.33) = 1 - 0.6293 = 0.3707

P-value = 2 * 0.3707 = 0.7414