Question

3. The dataset RestaurantTips contains data recorded from 157 restaurant bills at a bistro in New York over a two week period and is considered to be representative of all bills at this particular restaurant. The mean tip was $3.849 and the standard deviation was 2.421. Using the methods of Section 6.2-CI (statistic t* (SE)), find and interpret a 90% confidence interval for the average tip given at this restaurant. Show all calculations.

Answer 1

90% Confidence Interval is
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 157- 1 ) = 1.655
3.849 ± t(0.1/2, 157 -1) * 2.421/√(157)
Lower Limit = 3.849 - t(0.1/2, 157 -1) 2.421/√(157)
Lower Limit = 3.5292
Upper Limit = 3.849 + t(0.1/2, 157 -1) 2.421/√(157)
Upper Limit = 4.1688
90% Confidence interval is ( 3.5292 , 4.1688 )

Interpretation = We are 90% confident that the average ti given at this restaurant is between

$3.5292 and $4.1688