RES 342 Practice Problems - Week 4
4. A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

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Company	Sales ($ millions)	Earnings (S millions)		Company	Sales ($ millions)	Earnings ($ millions)	
Papa John's International	89.2	4.9		Checkmate Electronics	17.5	2.6	
Applied Innovation	18.6	4.4		Royal Grip	11.9	1.7	
Integracare	18.2	1.3		M-Wave	19.6	3.5	
Wall Data	71.7	8.0		Serving-N-Slide	51.2	8.2	
Davidson Associates	58.6	6.6		Daig	28.6	6.0	
Chico's Fas	46.8	4.1		Cobra Golf	69.2	12.8	
a.	Compute the correlation coefficient.
b.	Compute the coefficient of determination.
c.	Determine the regression equation.
d.	For a small company with $50.0 million in sales, estimate the earnings.

The following hypotheses are given.
H0:  CT] < a2	//): <J] > <T2
A random sample of five observations from the first population resulted in a standard deviation of 12.1
A random sample of seven observations from the second population showed a standard deviation of 7.   j
At the .01 significance level, is there more variation in the first population?	._/
Stargell Research Associates conducted a study of the radio listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes per day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women?

A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks
as 12.6 percent with a standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent. At the .05 significance level, can we conclude that there is more variation in the oil stocks?

1.

17=82.9
a)	n=12    £AT =107
IF2 = 615.29
12(712.9)-(107X82.9)
r =
V[12(1009)-(107)2][12(615.29)-(82.9)2]
b)	0.296, found by (-0.544)2

= -0.544