Chapter 7, Problem 88CRE

Technology Anxiety In a 2018 survey conducted by Northeastern University, $28\%$ of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a $95\%$ confidence interval with a margin of error of 3 percentage points.

a. Report the confidence interval for the proportion of adults with education level less than a bachelor’s degree who are worried about job loss due to new technology or automation.

b. If the sample size were smaller and the sample proportion stayed the same, would the resulting interval be wider or narrower than the one obtained in part a?

c. If the confidence level were $99\%$ rather than $95\%$ and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a?

d. In 2018 the population of the United States was roughly 327 million. If 50 million people were added to the population what effect, if any, would this have on the intervals obtained in this problem?