Question

1) Identify the rejection point(s) for the test of the following hypothesis:

H0: mean = 10, Ha: mean != 10

Conducted on a sample size of 15, on a normally distributed population with unknown population variance, and a desired Type1 error probability (alpha) of 0.05.

Hint: use the appropriate statistical function in your spreadsheet to determine the rejection point.

Z test with rejection points -1.64 and +1.64

Z test with rejection points -1.96 and +1.96

t-test with degrees of freedom=14, and rejection points -2.14 and +2.14

2) Identify the rejection point(s) for the test of the following hypothesis:

H0: mean = 10, Ha: mean != 10

Conducted on a sample size of 20, on a normally distributed population with known population variance, and a desired Type1 error probability (alpha) of 0.01.

Hint: use the appropriate statistical function in your spreadsheet to determine the rejection point.

z-test with rejection points of -2.33 and +2.33

z-test with rejection points of -2.58 and +2.58

t-test with degrees of freedom=19 and rejection points of -2.54 and +2.54

3)Identify the rejection point(s) for the test of the following hypothesis:

H0: mean <= 10, Ha: mean > 10

Conducted on a sample size of 25, on a normally distributed population with unknown population variance, and a desired Type1 error probability (alpha) of 0.10.

Hint: use the appropriate statistical function in your spreadsheet to determine the rejection point.

z-test with rejection point of -1.64

t-test with degrees of freedom = 24 and rejection point of -1.32

t-test with degrees of freedom = 24 and rejection point of -1.71

4) You want to determine whether the returns variance of one investment vehicle is different than another. To do this you have collected a sample of 120 monthly returns for each vehicle, and found that the variance of Investment 1 is 20 and the variance of Investment 2 is 25.

Construct the hypothesis, decide on the appropriate test statistic to calculate, and compute the rejection points using alpha of 0.05.

What is the test statistic and rejection points for the test? Can you reject the null hypothesis of equal variances?

F test, with degrees of freedom of 119 and 119, and rejection points of 0.70 and 1.43. Cannot reject the null.

F test, with degrees of freedom of 119 and 119, and rejection points of 0.70 and 1.43. Reject the null.

t-test, with degrees of freedom of 238, and rejection points of -1.97 and +1.97. Reject the null

5) You want to determine if a mutual fund's assets under management (AUM) is correlated with the fund's excess return. To do this you collect the following data for 5 mutual funds:

Fund	AUM (million)	Return (%)
1	33.1	10.1
2	40.5	12.2
3	22.8	11.2
4	15.2	9.6
5	58.7	6.8

Your null hypothesis is that there is no correlation. Calculate the Spearman rank correlation coefficient, and make a decision on your hypothesis based on Table 11 in the text.

Based on rejection points of -0.8 and +0.8, and the spearman coefficient of -0.26, do not reject the null

Based on rejection points of -0.9 and +0.9, and the spearman coefficient of 1.64, reject the null

Based on rejection points of -0.9 and +0.9, and the spearman coefficient of -0.1, do not reject the null

Answer 1

1)
since population variance is unknown and sample size is less than 30
t-test will be used
df =n-1 = 14

two-tailed test

rejection points are 2.14 and -2.14

hence option C) t-test with degrees of freedom=14, and rejection points -2.14 and +2.14 is correct
2)
here population variance is known
hence z-test is used

alpha = 0.01

two-tailed
hence
option B)z-test with rejection points of -2.58 and +2.58

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