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. Use Table 2. Months Closing Stock Price January 2010 $222 February 2010 225 March 2010 229 April 2010 224 May 2010 220 June 2010 228 SOURCE: http://finance.yahoo.com. a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places and "Sample mean" and "Sample standard deviation" to 2 decimal places.) Sample mean Sample standard deviation b. Compute the 99% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed. (Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval to c. What happens to the margin of error if a higher confidence level is used for the interval estimate? The margin of error decreases as the confidence level increases. The margin of error increases as the confidence level increases.

Answer 1

a) = (222 + 225 + 229 + 224 + 220 + 228)/6 = 224.67

s = sqrt(((222 - 224.67)^2 + (225 - 224.67)^2 + (229 - 224.67)^2 + (224 - 224.67)^2 + (220 - 224.67)^2 + (228 - 224.67)^2)/5) = 3.44

b) At 99% confidence interval the critical value is t^* = 4.033

The 95% confidence interval for population mean is

+/- t^* * s/

= 224.67 +/- 4.033 * 3.44/

= 224.67 +/- 5.66

= 219.01, 230.33

c) The margin of error increases as the confidence level increases.