Question

With some interest in running your own Pizza store and a decent credit rating, you can probably get a bank loan for franchises such as Dominoz Pizza, Pizza Hut, Pappa Johns, and Little Caesar's. Startup costs (in thousands of dollars) for a random sample of Pizza stores are given below. Assume start up costs follow an approximately normal distribution.

85, 100, 129, 75, 95, 94, 116, 173, 95

A) Find a 90% Confidence Interval for the population mean startup cost μ for Pizza store franchises. Name the Confidence Interval.

B) State a Conclusion in a complete sentence about the meaning of this confidence interval and use the appropriate wording for the 3 parts

Answer 1

A) Sample mean(xbar) = (85 + 100 + 129 + 75 + 95 + 94 + 116 + 173 + 95) / 9 = 106.899

Sample standard deviation(s) = [(85 - 106.899)^2 + (100 - 106.899)² + .....................+ (95 - 106.899)² ] / 9 - 1

= 29.442

sample size(n) = 9

T critical value = 1.86 on 8 degrees of freedom at 90% confidence level

now

90% confidence interval for the population mean startup cost μ for Pizza store franchises.

= (xbar +/- tc*s/sqrt(n))

= (106.889 +/- 1.86*29.442 / sqrt(9))

= (88.64, 125.15)

b) It is 90% confident that the population mean startup cost μ for Pizza store franchises lies between (88.64 and 125.15)