Question

Golf cart attendants at a local country club often receive tips from golfers they assist with golf clubs. To help recruit new​ employees, the country club would like to determine the average tips per day an attendant earns. A sample of 27 attendants averaged ​$34.21 per day in tips. Assume the population standard deviation for daily tips is ​$7.58. Complete parts a and b below.

a. Construct a 90​% confidence interval to estimate the average daily tips for an attendant.

Answer: The average daily tips for an attendant is between a lower limit of ​$31.81 and an upper limit of ​$36.61.

b. What assumptions need to be made to construct this​ interval?

Answer: When the sample size is less than 30 and the population standard deviation is​ known, an assumption needs to be made about the population in order to calculate a confidence interval. Review the Central Limit Theorem to determine what assumption is necessary.

Above are the questions and answers. Please provide all Excel formulas (not calculations) that get to these answers.

Answer 1

Solution-A:

margin of error in excel

=CONFIDENCE.NORM(0.1,7.58,27)

=

2.399466

lower limit=xbar-MOE=34.21-2.399466=31.81053=31.81

upper limit=xbar+MOE=34.21+2.399466= 36.60947=36.61

b. What assumptions need to be made to construct this​ interval?

sample to be independent

and

simple random sample

sample should follow normal distribution

Accordinf to central limit theorem for large sample ,n>30 sample follows normal distribution

here n=27

since popualtion distribution is not knowm ,we cannot assume distribution as normal

conditions not met