Suppose a researcher studying annual expenditures on lipstick wishes to have a 95% confidence interval level (z=1.96) and a sampling error of less than $3. Answer the question below and show all your work. a) If the estimate of the standard deviation (S) is $35 based on a pilot study, what is the required sample size (n)?

b) What is the required sample size if the researcher is okay with a range of acceptable error of $6? What is your interpretation compared to when the acceptable sampling error was $3?

c) The researcher estimates the cost of data analysis to be $3,000, and the cost of an online customer survey to be $5 per customer. What is the maximum affordable sample size if the research budget is $5,000 for data collection and analysis?