Question

The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. [You may find it useful to reference the t table.]

Months Closing Stock Price

January 90, February 95, March 96, April 99, May 91, June 93

a. Calculate the sample mean and the sample standard deviation.

b. Calculate the 95% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed.

Confidence interval ________ to ________

c. What happens to the margin of error if a higher confidence level is used for the interval estimate?

Answer 1

A)

sample mean, xbar = 94
sample standard deviation, s = 3.3466

B)

sample size, n = 6
degrees of freedom, df = n - 1 = 5

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.571

ME = tc * s/sqrt(n)
ME = 2.571 * 3.3466/sqrt(6)
ME = 3.513

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (94 - 2.571 * 3.3466/sqrt(6) , 94 + 2.571 * 3.3466/sqrt(6))
CI = (90.49 , 97.51)

C)

margin of errro increases as the confiednce level increases