Textbook Problem

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The price per share of stock for a sample of 25 companies was recorded at the beginning of 2012 and then again at the end of the 1st quarter of 2012 (The Wall Street Journal, April 2, 2012). How stocks perform during the 1st quarter is an indicator of what is ahead for the stock market and the economy. Use the sample data in the file entitled StockPrices to answer the following.

1. a. Let d_i denote the change in price per share for company i where d_i = 1st quarter of 2012 price per share minus the beginning of 2012 price per share. Use the sample mean of these values to estimate the dollar amount a share of stock has changed during the 1st quarter.
2. b. What is the 95% confidence interval estimate of the population mean change in the price per share of stock during the first quarter? Interpret this result.

To determine

Find the estimate of the dollar amount of stock changed by a share during the 1^st quarter using the sample mean of these values.

Explanation of Solution

Calculation:

For a sample of 25 companies, price per share of stock are recorded at the beginning of 2012 and again recorded at the end of the 1^st quarter of 2012.

Here, $\text{Difference}={\text{1}}^{\text{st}}\text{ quarter price per share}-\text{beginning of year price per share}$

The difference values for each of the 25 elements are tabulated below:

End of 1st Quarter	Beginning of Year	d
24.13	19.91	$24.13-19.91=4.22$
38.01	37.36	$38.01-37.36=0.65$
52.9	45.78	$52.9-45.78=7.12$
58.42	62.03	$58.42-62.03=-3.61$
65.96	65.58	$65.69-65.58=0.38$
107.48	105.94	$107.48-105.94=1.54$
30.01	23.71	$30.01-23.71=6.3$
12.45	10.71	$12.45-10.71=1.74$
43.41	41.22	$43.41-41.22=2.19$
20.07	17.91	$20.07-17.91=2.16$
31.23	30.24	$31.23-30.24=0.99$
21.15	18.08	$21.15-18.08=3.07$
50.31	42.04	$50.31-42.04=8.27$
45.98	33.25	$45.98-33.25=12.73$
67.21	66.71	$67.21-66.71=0.5$
38.23	40.12	$38.23-40.12=-1.89$
71

To determine

Obtain the 95% confidence interval estimate of the population mean change in the price per share of stock during the first quarter and interpret.