Question

1. Due to the current pandemic, a research firm in Brazil would like to study whether grocery store hiring is up from previous years, but is unable to collect data from each and every establishment in the country. Based on a random sample of 25 stores throughout the country, they calculate that the sample standard deviation of the number of workers per store is 10.7258 people.

a. If the research firm uses the mean calculated from the sample of 25 stores, what is the probability that they are within 6 people of the true population mean number of workers?

b. Suppose the firm would like to be accurate to within 1 person. How many people should they sample?

Answer 1

1a)

Given ,

Margin of error = 6

This is the critical value of z , we have to find corresponding confidence level

From Standard Normal table we find that

P( -2.80< z < 2.80) = 0.9948

Thus , Probability that they are within 6 people of true population mean number of workers = 0.9948 or 99.48%

b) Given

Margin of error = 1

   

( we use zc = 2.80 , as calculated above)

Sample size required = 902