Question

1. You are planning an evaluation of a semester-long alcohol awareness campaign at your college. Previous evaluations indicate that about 37% of the students surveyed will respond "Yes" to the question "Did the campaign alter your behavior toward alcohol consumption?" How large a sample of students should you take if you want the margin of error to be within 9 percentage points with 95% confidence?

2. Suppose a large telephone manufacturer that entered the post-regulation market quickly has an initial problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 4 percentage points with 80% confidence? Use three decimal places for the critical value.

Answer 1

Q.1) Given that, previous estimate = p = 0.37

margin of error ( E ) = 9% = 0.09

A 95% confidence level has significance level = 0.05 and critical value is,

We want to find, the sample size ( n ),

Required sample size is 111

Q.2) margin of error ( E ) = 4% = 0.04

No previous estimate is given so, we assume p = 0.5

A 80% confidence level has significance level = 0.05 and critical value is,

We want to find, the sample size ( n ),

Required sample size is 257

Note: If we take critical value is for 80% confidence level then sample size is 256.