4. Problem 4. 36 points Conduct a two-tailed hypothesis test given the informati
ID: 3436920 • Letter: 4
Question
4. Problem 4. 36 points
Conduct a two-tailed hypothesis test given the information below.
Assume that the population standard deviations are equal for income mutual funds and growth mutual funds. Use the following sample data to test whether there is a difference in the mean yields of the two funds at the 0.05 level of significance.
Income
Growth
Sample Size
35
40
Sample Mean
900
875
Sample Standard Dev
35
45
What is the null hypothesis?
What is the computed value of the test statistic t?
What is the p value for this test statistic?
What decision is made about the null hypothesis using an = 0.05?
Income
Growth
Sample Size
35
40
Sample Mean
900
875
Sample Standard Dev
35
45
Explanation / Answer
Null Hypothesis : mu(income) = mu(growth)
Alternate Hypothesis : mu(income) not= mu(growth)
t = ( 900 - 875) / sqrt(35^2/35 + 45^2/40) = 2.70
Two tailed test , therefore
P value = 2 ( 1- 0.9965) = 0.007
0.007<0.05 Hence Failed to reject null hypothesis.
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