Question

A random sample of construction workers was taken in a large city. Of the 125 workers sampled, 21 were unemployed. We wish to construct a 99% confidence interval for the proportion of unemployed construction workers in this city. Assume all assumptions and conditions are met.

Part 1 - find the sample proportion

part 2 What critical value would you use to be 99% confident?

Part 3 Use the appropriate formula to build the confidence interval.

Part 4 If we wanted to reduce the Margin of Error to 3% and keep a 99% confidence level, what minimum sample size should we use for the survey? assume p is unknown.

Answer 1

Soln,

Given that 125 workers were sampled hence n=125 out of which 21 were unenployed, hence x= 21

also give Confidence level =99 %

1. Hence the Sample proportion

2. The critical value used for99 % confidence level Z_c= 2.58

can be seen through table of Z critical at 99 % confidence level.

3. The Confidence Interval formula for population proportion of unemployed workers

, Where E can be found by

So Confidence interval

4. If We want to Reduce Error to 3 % level or at 0.03 at 99 % confidence leve

So a minimum of 1044 sample is needed to reduce error to 3 % .