Problem#20.  Confidence Interval for a Population Proportion

NOTE: Show all your work in Excel. 

a) Given sample size n=100, significance level a=0.05, and  sample proportion p ̅=0.75. 

Compute a 95% confidence interval for the population proportion using Excel. 

Interpret the confidence interval.

b) Given sample size n=300, significance level a=0.08, and  sample proportion p ̅=0.90. 

Compute a 92% confidence interval for the population proportion using Excel. 

Interpret the confidence interval.

Problem#21.  Confidence Interval for a Population Proportion

A survey was sent to members of a small business association. Two hundred and fifty business professionals responded to the survey.  190 of the survey respondents said they were 25 years or older when they started their first business. 35 of the survey respondents said they currently own a business that employs 20 or fewer people.   

NOTE: Show all your work in Excel.

a) What is the 90% confidence interval for the population proportion of business professionals who started their first business when they were 25 years or older? Interpret the confidence interval.

b) What is the 99% confidence interval for the population proportion of business professionals who own a business that employees 20 or fewer employees? Interpret the confidence interval.

Problem#22.  Confidence Interval for a Population Proportion

A survey was sent to members of a small business association. 30% of the survey respondents said they were 25 years or older when they started their first business. 73% of the survey respondents said their business employs 20 or fewer employees. 

NOTE: Show all your work in Excel. 

a) Suppose the sample size is 200. What is the 90% confidence interval for the population proportion of business professionals who started their first business when they were 25 years or older? Interpret the confidence interval.

b) Suppose the sample size is 500. What is the 90% confidence interval for the population proportion of business professionals who own a business that employees 20 or fewer employees? Interpret the confidence interval.

c) Compare the confidence intervals in parts a and b. How did the sample size affect the margin of error?  Is the confidence interval in part b wider or narrower  than the one in part a?