Question

Is college worth it? Among a simple random sample of 334 American adults who do not have a four-year college degree and are not currently enrolled in school, 144 said they decided not to go to college because they could not afford school.

1. Calculate a 99% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places.

( ,  )

2. Suppose we wanted the margin of error for the 99% confidence level to be about 2.75%. What is the smallest sample size we could take to achieve this? Note: For consistency's sake, round your z* value to 3 decimal places before calculating the necessary sample size.

Choose n=

Answer 1

Given that, sample size ( n ) = 334 and x = 144

1) Using TI-84 calculator, we get 99% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is,

( 0.3613, 0.5009 )

That means, we are 99% confident that, the proportion of Americans who decide to not go to college because they cannot afford it is between 0.3613 and 0.5009

2) Given that, margin of error ( E ) = 2.75% = 0.0275

99% confidence level has critical value is,

We want to find the sample size ( n ),

Required sample size is n = 2150

Note: if you want to sample size is nearest to next whole number then n = 2151