Question

In a recent study at a local college, 48 students admitted that they had tried alcohol at least once while under the legal drinking age, while only 4 students said they had not. Is there enough data to conduct a hypothesis test to see if the percentage of students at the college who admit to drinking underage is the same as the national percentage of 95%? Show work.

Answer 1

I ) Null hypothesis Ho : p = 0.95 ( claim)

Alternative hypothesis H1 : p 0.95

II) Test statistic Z

Z = ( p^ - p)/ sqrt [ p *(1-p)/n]

Where n = 52 and p^ = 48/52 = 0.92

Z = (0.92 - 0.95)/sqrt [ 0.95*0.05/52]

Z test = -1.00

III) critical value for a = 0.05 and two tailed test

Zcritical = Z​​​​​​0.025 = +/- 1.96

IV) Decision rule : Reject the null hypothesis Ho if Z < Zcritical or Z > Zcritical , otherwise fail to reject the null hypothesis

Our Z = -1.00 > -1.96

Conclusion : Fail to reject the null hypothesis . There is sufficient evidence to support the claim thatthat percentage of students at the college who admit to drinking underage is the same as the national percentage of 95%