The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.

(4) Calculate a 95% confidence interval estimate for the population proportion of college students who work to pay for tuition and living expenses.

Hint: Refer to Section 8.4 in your textbook, and use NORM.INV in Excel to find the z value.

(4) Calculate a 99% confidence interval estimate for the population proportion of college students who work to pay for tuition and living expenses.

(3) Use your answers to parts (a) and (b) to describe what happens to the margin of error as the confidence is increased from 95% to 99%. Explain why this makes sense intuitively.