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

(a)

Sample proportion, p = 97 / 185 = 0.5243

Standard error of the proportion, SE =

= 0.0367

Z value for 90% level of Confidence is 1.645

Margin of error = Z * SE = 1.645 * 0.0367 = 0.0604

90% confidence interval of the true proportion is,

(0.5243 - 0.0604, 0.5243 + 0.0604)

(0.4639, 0.5847)

Since, 0.4 (40%) does not fall in the 90% confidence interval of the true proportion, it is unbelievable 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)

Since values greater than 0.45 (45%) fall in the 90% confidence interval of the true proportion, it is 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%.