In a random sample of 20 people, the mean tip that they said they would leave after a $30 meal was X bar = $3.75 and the standard deviation was s = $0.50.

Question

Assuming that tips are normally distributed, construct a 99% confidence interval on the population mean tip µ

Answer 1

The critical value for 99% confidence level is 2.861. The standard error is 0.5/√20. 19 degrees of freedom are used to find the critical t value from tables.

The confidence interval is 3.75±2.861×0.5/√20, that is, 3.75±0.32, putting the tip between $3.43 and $4.07.

This corresponds to 11.4% and 13.6% approx.