Question

a. It is conjectured that among all colleges and universities, the proportion that will move their fall 2020 classes online is 0.17. Some states have been hit harder by COVID-19 than others, so it is conjectured that the proportion of all colleges and universities who will move their fall 2020 classes online is greater than 0.17. State the appropriate null and alternative hypotheses that should be tested. b. A simple random sample of 60 colleges and universities is selected, and 18 indicated they will move their fall 2020 classes online while the other 42 indicated they did not plan to move their fall 2020 classes online. If appropriate, use this information to test the hypotheses stated in question (a) at the a= .05 level of significance.

Answer 1

Solution:

a)

The null and alternative hypothesis are

H₀ : p = 0.17

vs

H_a : p > 0.17

b)

n = 60

x = 18

Let  $url=https://latex.codecogs.com/gif.latex?%5Chat%20p&t=1596156541&ymreqid=50870fb5-0ab3-84d7-1c0d-d8002a010800&sig=JlfgkQ0bC7ZEGQ_ThsKjWQ--~D$ be the sample proportion.

$url=https://latex.codecogs.com/gif.latex?%5Chat%20p&t=1596156541&ymreqid=50870fb5-0ab3-84d7-1c0d-d8002a010800&sig=JlfgkQ0bC7ZEGQ_ThsKjWQ--~D$ = x/n = 18/60= 0.3

The test statistic z is

z =   $url=https://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Chat%20p-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D&t=1596156541&ymreqid=50870fb5-0ab3-84d7-1c0d-d8002a010800&sig=Mb35q3ecYx_BXU4ND8pkOQ--~D$

=  (0.3 - 0.17)/$\sqrt{}$[0.17*(1 - 0.17)/60]

= 2.68

Test Statistic z = 2.68

> sign in Ha indicates that the test is "RIGHT TAILED"

For right tailed z test ,

p value = P(Z > z) = P(Z > 2.68) = 1 - P(Z < 2.68) = 1 - 0.9963 = 0.0037

p value = 0.004

Decision :

p value is less than given significance level α = 0.05

Reject the null hypothesis .