Question

Psychologists studied the size of the tip in a restaurant when a message indicating that the next day's weather would be good was written on the bill. Data below gives info on the tips for 20 patrons, measured in percent of the total bill. Past experience with patrons of the restaurant indicate a stdev sigma = 2. Construct and Interpret a 95% confidence interval for the mean percentage tip for all patrons of this restaurant when they receive a message on their bill indicating that the next day's weather will be good. tip%s 20.8 24.9 18.7 22.3 19.9 27.0 20.6 20.4 21.9 22.2 23.4 24.0 22.8 21.1 24.9 22.1 22.2 22.0 20.3 22.7

Answer 1

Sample size = n = 20

Sample mean = = 22.21

Population standard deviation = = 2

We have to construct 95% confidenc interval for the population mean.

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

z confidence interval

Here E is a margin of error

Zc = 1.96 ( Using z table)

So confidence interval is ( 22.21 - 0.876539 , 22.21 + 0.876539) = > ( 21.3335 , 23.0865)

Interpretation: We are 95% confidence that population mean lies into given interval.