4 Problem 4 36 points Conduct a twotailed hypothesis test gi

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?

Solution

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.