Chapter 13, Problem 11SE

Circuit City (Example 2) A statistics student who worked as a cashier at the (former) electronics superstore Circuit City wanted to estimate the amount spent by customers using either credit or debit cards. She took a random sample of customers and recorded the amount they spent. Figure A shows a histogram of the data.

a. Figure B shows a $$95\%$$confidence interval for the mean amount spent. Interpret this confidence interval.

b. A log transform of the data shows a more Normally distributed data set. Figure C shows a $$95\%$$confidence interval for the log (base 10) of the amounts spent. Convert the boundaries back into dollars by raising 10 to the power given as the boundary. Report and interpret the confidence interval for the geometric mean.

c. Which interval is narrower?

d. Which interval would you report if you wanted to tell a Circuit City manager about the typical amount of money spent via credit or debit cards? Explain.