Question

Directions: Show ALL work! Please round any answer to the nearest hundredth, unless you can get an exact amount. If an answer asks to explain, please make sure to give a valid and complete explanation. For your hypothesis tests, make sure you give a complete interpretation.

1. You work for Globo Gym and want to estimate the population mean cost of belonging to a gym in the surrounding areas. As part of your study, you randomly select 45 gyms and find the mean for belonging to a gym to be $250/year. Assume the population standard deviation is $30.

a)   Construct a 95% confidence interval for the population mean cost of belonging to a gym. Interpret the results.

b)   Using the information from part a, determine the minimum sample size required to be 99% confident that the sample mean gym membership cost is within $10 of the population mean gym membership cost.

Answer 1

a)

95% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

250 - 1.96 * 30 / sqrt(45) < < 250 + 1.96 * 30 / sqrt(45)

241.23 < < 258.77

95% CI is ( 241.23 , 258.77 )

b)

Minimum sample size = (Z/2 * / E)²

= (2.5758 * 30 / 10)²

= 59.71

Sample size = 60 (Rounded up to nearest integer)