Question

	For the following Hypothesis Tests below :
		(a) State the null hypothesis, if not given.
		(b) State the decision rule.
		(c) Compute the value of the test statistic.
		(d) What is your decision regarding H0?
		(e) Your conclusion.

Exercise 6: A stockholder at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 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. A the .05 significance level, can we conclude that the variations are different?

(a) Ho:

(b) Reject Ho when

(c) F =

(d) Ho is

(e)

Answer 1

Let , be the variance of oil stocks and utility stocks respectively.

(a)

H0: =

H1:

(b)

Numerator degree of freedom, df1 = 10 - 1 = 9

Denominator degree of freedom, df2 = 8 - 1 = 7

For two tail test, the significance level are 0.05/2 = 0.025 and 1 - 0.05/2 = 0.975

Critical value of F at 0.025 and 0.975 with degree of freedom 9, 7 are 0.24 and 4.82

Reject Ho when F < 0.24 or F > 4.82

(c)

F = s1² / s2²

= 3.9² / 3.5²

= 1.24

(d)

Since 0.24 < F < 4.82, H0 is accepted.

(e)

We fail to reject H0 and conclude that there is no significant evidence that the variations of  oil stocks and utility stocks are different