Question

The Simcoe County Food Emporium claims that "the typical customer spends $65 per visit." A sample of 12 customers revealed the following purchases, in dollars, spent last visit: $61 66 63 63 64 65 62 60 56 67 63 58 a. What is the point estimate of the population mean? (Round the final answer to 2 decimal places.) Point estimate $ b. Develop a 90% confidence interval for the population mean. (Round the final answers to 2 decimal places.) The confidence interval for the population mean is between $ and $ . c. Is the restaurant’s claim that the "typical customer" spends $65 per visit reasonable?

Answer 1

a)

point estimate sample mean, xbar = 62.33

b)

sample standard deviation, s = 3.2004
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.796

ME = tc * s/sqrt(n)
ME = 1.796 * 3.2004/sqrt(12)
ME = 1.659

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (62.33 - 1.796 * 3.2004/sqrt(12) , 62.33 + 1.796 * 3.2004/sqrt(12))
CI = (60.67 , 63.99)

c)

yes, because confidence interval does not contain 65