Question

A simple random sample of 300 colleges and universities was selected and for each it was determined whether they planned to move summer 2020 classes online or not. Of the 300 colleges and universities in the sample, 90 responded that they will move summer 2020 classes online , and 210 responded that they will not move summer 2020 classes online. . If appropriate, use this information to calculate and interpret a 99% confidence interval for the proportion of all colleges and universities that will move their summer 2020 classes online . Please type your solution in the box below.

Answer 1

Solution :

Given that,

n = 300

x = 90

Point estimate = sample proportion = = x / n = 90 / 300 = 0.30

1 - = 1 - 0.30 = 0.70

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 (((0.30 * 0.70) /300 )

= 0.068

A 99% confidence interval for population proportion p is ,

± E

= 0.30  ± 0.068

= ( 0.232, 0.368 )

We are 99% confident that the true proportion of all colleges and universities that will move their summer 2020 classes online between 0.232 and 0.368.