Question

A simple random sample of 80 colleges and universities is selected, and 16 indicated will move their summer 2020 classes online while the other 64 indicated they did not plan to move their summer 2020 classes online . If appropriate, use this information to test the hypotheses stated in question 10 at the a = .10 level of significance. Please type your answer in the box below.

Hypothesis: H0:   π = 0.14 versus HA: π > 0.14

Answer 1

Solution:

Given:

Sample size= n = 80

x = Number of colleges and universities indicated will move their summer 2020 classes online = 16

Level of significance= 0.10

We have to test the hypothesis: H0:   π = 0.14 versus HA: π > 0.14

This is right tailed test.

Since n*p = 80*0.14 = 11.2 > 10 and n*(1-p) = 80 * ( 1 -0.14)= 68.8 > 10, we can use Central Limit Theorem for using Normal approximation to Proportion.

Find test statistic:

where

thus

Find z critical value:

For right tailed test , find Area = 1 - 0.10 = 0.90

Look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z critical value = 1.28

Decision Rule:
Reject null hypothesis ,if z  test statistic value > z critical value = 1.28, otherwise we fail to reject H0.

Since z  test statistic value = 1.55 > z critical value = 1.28, we reject null hypothesis H0.

Thus we conclude that: the true population proportion of colleges and universities indicated will move their summer 2020 classes online is more than 0.14.