The monthly closing stock prices (rounded to the nearest dollar) for Panera Brea

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. 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 95% 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.

Explanation / Answer

a. The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

Mean=Sum of terms/Number of terms=235.1667

Create the following table.

Find the sum of numbers in the last column to get.

(xiX¯)2=50.8333

Calculate using the above formula.

=Sqrt((xiX¯)2/n-1)

=3.1885

b. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So E=z*sd/sqrt(n)=2.551

Hence CI=mean+/-E=235.167+/-2.551=(232.616,237.718)

c. As confidence level increases E increase because z value will increase.

So answer is The margin of error increases as the confidence level increases

data data-mean (data - mean)2 232 -3.1667 10.02798889 236 0.8333 0.69438889 235 -0.1667 0.02778889 239 3.8333 14.69418889 238 2.8333 8.02758889 231 -4.1667 17.36138889

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