Question

Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the WEBfile named Houston. Based upon past studies the population standard deviation is known with = $14. Click on the webfile logo to reference the data. Round your answers to THREE decimal places. a. At 99% confidence, what is the margin of error? b. Develop a 99% confidence interval estimate of the mean amount spent for lunch. ____ to ____ Amount 20.50 14.63 23.77 29.96 29.49 32.70 9.20 20.89 28.87 15.78 18.16 12.16 11.22 16.43 17.66 9.59 18.89 19.88 23.11 20.11 20.34 20.08 30.36 21.79 21.18 19.22 34.13 27.49 36.55 18.37 32.27 12.63 25.53 27.71 33.81 21.79 19.16 26.35 20.01 26.85 13.63 17.22 13.17 20.12 22.11 22.47 20.36 35.47 11.85 17.88 6.83 30.99 14.62 18.38 26.85 25.10 27.55 25.87 14.37 15.61 26.46 24.24 16.66 20.85

Answer 1

Sample size = n = 64

Sample mean = = 21.52

Population standard deviation = = 14

a) Confidence level = 0.99

E is a margin of error

Zc = 2.58 ( Using z table)

b) We have to construct a 99% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

So confidence interval is ( 21.52 - 4.515 , 21.52 + 4.515) = > ( 17.005 , 26.035)