Question

A sample of data is collected from the University's Undergraduate Advising Center. Records from this sample of data show that in the Spring 2019 semester, there were 185 students who rescheduled their advising appointments 2 or more times. Of these students, 97 were unable to enroll in a required course for the following semester. Answer the following questions using a 90% level of Confidence (a) Is it believable that the true proportion of these students (those who rescheduled their advising appointments 2 or more times) that are unable to enroll in a required course, is equal to 40%? (b) Is it believable that the true proportion of these students (those who rescheduled their advising appointments 2 or more times) that are unable to enroll in a required course, is greater than 45%?

Answer 1

Sample size, n = 185

Favorable outcome, x = 97

Sample proportion, p̄ = x/n = 0.5243

90% Confidence interval :

At α = 0.10, two tailed critical value, z crit = NORM.S.INV(0.1/ 2) = 1.645

0.5243 0.4757 0.5243 1.645 185 ( 0.4639 , 0.5847)

a) As the proportion 0.40 is not in the confidence interval range . so we reject the null hypothesis.

There is not enough evidence to claim that the true proportion of these students that are unable to enroll in a required course is equal to 40% at 0.10 significance level.

b) The value in confidence interval both are greater than 45%, so we can claim that true proportion of these students that are unable to enroll in a required course is greater than 45% at 0.10 significance level.