Chapter 16 Question 38 Hiring - In preparing a report on the economy, we need to

Question

Chapter 16 Question 38 Hiring - In preparing a report on the economy, we need to estimate the percentage of a. How many randomly selected employers must we contact in order to create an b. Suppose we want to reduce the margin of error to 3%, what sample size would c. Why might it not be worth the effort to try to get an interval with a margin of businesses that plan to hire additional employees in the next 60 days. estimate in which we are 98% confident with a margin of error of 5%? suffice? error of only 1%?

Explanation / Answer

Solution:

a) Given that p = q = 0.5
Confidence level = 0.98 => Z/2 = 2.33
Margin of Error E = 0.05
Sample size n = (Z/2/E)^2*pq
= (2.33/0.05)^2 (0.5)(0.5)
= 542.8 543
b) given that p = q = 0.5
Confidence level = 0.98 => Z/2 = 2.33
Given E = 0.03

Sample size n = (Z/2/E)^2*pq
= (2.33/0.03)^2 (0.5)(0.5)
= 1508.03
1509

c) Given that margin of error = 1% or 0.01
For 98% confidence interval, the critical value Z/2 = 2.33
Sample size n = (Z/2/E)^2*pq
= (2.33/0.01)^2 (0.5)(0.5)
= 13572.25 13573

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