Six years ago it was determined that 81 of all seniors at Up

Six years ago, it was determined that 81% of all seniors at Upper Midwest University hadchanged majors at least once. A new pre-enrollment advising program was designed to reducethe proportion of students who change majors, and thus, decrease the time until they graduate.To test whether the program has reduced the proportion of students who change majors, randomsample of 300 seniors from the class of 2015 was selected and 228 had changed majors at leastonce.

(a)Compute the p-value.

(b)State a conclusion in terms of the problem above at the 5% significance level.

Solution

(a)Compute the p-value.

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(228/300-0.81)/sqrt(0.81*(1-0.81)/300)

=-2.21

It is a left-tailed test.

So the p-value= P(Z<-2.21) =0.0136 (from standard normal table)

-------------------------------------------------------------------------------------------------------------

(b)State a conclusion in terms of the problem above at the 5% significance level.

Since the p-value is less than 0.05, we reject the null hypopthesis.

So we can conclude that he program has reduced the proportion of students who change majors