Question

Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence?

Answer 1

1727 students

Explanation:

Here we have the formula for sample size given as

`n = (p(1-p)z^2)/(ME^2)`

Where:

p = Mean

ME = Margin of error = 3

z = z score

Therefore, we have

p = 150/240 = 0.625

z at 99 % = 2.575

ME =
`\pm`3%

Therefore
`n = (0.625(1-0.625)2.575^2)/(0.03^2) = 1726.73`

The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.