Question

A school has 3400 students. They conduct a random sample of 124 students and find that 38 of them hate the school.

About how many students should the school predict hate the school?


a 1040

b 890

c 1220

d 950

Answer 1

a) We need a sample size of at least 2401.

b) We need a sample size of at least 1936.

Explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

(a) you are unwilling to predict the proportion value at your school and​

We use , which is when we are going to need the largest sample size.

So we need to find We need a sample size of at least 2401.

(b) you use the results from the surveyed school as a guideline.

Now the same calculation, just with . So

We need a sample size of at least 1936.