Question

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. How stocks perform during the 1st quarter is an indicator of what is ahead for the stock market and the economy. The sample data are provided below. Construct a spreadsheet to answer the following questions.

End of 1st Quarter	Beginning of Year
26.83	18.71
40.41	34.86
54.80	44.18
59.52	59.53
67.36	62.98
109.08	104.14
31.91	21.61
14.15	8.91
45.21	39.12
21.37	15.91
32.93	28.54
22.75	15.88
52.51	39.94
48.28	31.65
69.01	65.31
39.23	37.42
72.92	59.90
41.67	39.56
33.36	24.26
76.21	66.97
69.06	51.90
88.53	82.96
24.45	20.14
31.96	24.48
108.81	104.50

a. Let di  denote the change in price per share for company i where di = 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

$ blank (to 2 decimals)

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.

Standard deviation (to 2 decimals):
Confidence interval (to 2 decimals):	(, )

The mean price per share has increase between blank % and blank % over the three-month period (to 1 decimal).

Answer 1

Solution:

Part 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

Thus we need to make following table:

End of 1st Quarter	Beginning of Year	di = 1st - begining
26.83	18.71	8.12
40.41	34.86	5.55
54.8	44.18	10.62
59.52	59.53	-0.01
67.36	62.98	4.38
109.08	104.14	4.94
31.91	21.61	10.3
14.15	8.91	5.24
45.21	39.12	6.09
21.37	15.91	5.46
32.93	28.54	4.39
22.75	15.88	6.87
52.51	39.94	12.57
48.28	31.65	16.63
69.01	65.31	3.7
39.23	37.42	1.81
72.92	59.9	13.02
41.67	39.56	2.11
33.36	24.26	9.1
76.21	66.97	9.24
69.06	51.9	17.16
88.53	82.96	5.57
24.45	20.14	4.31
31.96	24.48	7.48
108.81	104.5	4.31

Thus the sample mean of these values to estimate the dollar amount a share of stock has changed during the 1st quarter is:

Part 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.

Formula:

where

Standard deviation is:

Thus we need to make following table:

End of 1st Quarter	Beginning of Year	di = 1st - begining	di^2
26.83	18.71	8.12	65.9344
40.41	34.86	5.55	30.8025
54.8	44.18	10.62	112.7844
59.52	59.53	-0.01	1E-04
67.36	62.98	4.38	19.1844
109.08	104.14	4.94	24.4036
31.91	21.61	10.3	106.09
14.15	8.91	5.24	27.4576
45.21	39.12	6.09	37.0881
21.37	15.91	5.46	29.8116
32.93	28.54	4.39	19.2721
22.75	15.88	6.87	47.1969
52.51	39.94	12.57	158.0049
48.28	31.65	16.63	276.5569
69.01	65.31	3.7	13.69
39.23	37.42	1.81	3.2761
72.92	59.9	13.02	169.5204
41.67	39.56	2.11	4.4521
33.36	24.26	9.1	82.81
76.21	66.97	9.24	85.3776
69.06	51.9	17.16	294.4656
88.53	82.96	5.57	31.0249
24.45	20.14	4.31	18.5761
31.96	24.48	7.48	55.9504
108.81	104.5	4.31	18.5761

Thus

Now find margin of Error:

where t_c is t critical value for c = 95% confidence level

df = n - 1 = 25 - 1 = 24

two tailed area = 1 - c = 1 - 0.95 = 0.05

Thus look in t table for df = 24 and two tail area = 0.05 and find t critical value:

t_c = 2.064

Thus

Thus

Thus

Standard deviation :

Confidence interval (to 2 decimals):

Thus The mean price per share has increase between 5.4% and blank 9.0% over the three-month period.