Question

32. An independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. They collected information on the percentage of the bill left as a tip for 25 randomly selected bills. The average tip was 18.3% of the bill with a standard deviation of 2.7%. a. Construct an interval to estimate the true average tip (as a percent of the bill) with 99% confidence. b. Interpret the interval, and state any assumptions that were made in the construction of the interval.

Answer 1

a) Degrees of freedom = n - 1 = 25 - 1 = 24

For 24 degrees of freedom and 99% confidence,

Critical t value = 2.797

Hence,

99% confidence interval will be:

18.3 +2.797 * 2.7/25

18.3±1.51

(16.79, 19.81)

b) Interpretation: We are 95% confident that the true average tip in the area is between 16.79% of bill and 19.81% of bill.

Assumption: Since sample size is small, it was assumed that population is approximately normally distributed.