Question

            A financial planner wants to compare the yield of income- and growth-oriented mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income-oriented and 40 growth-oriented funds. The mean increase for a two-year period for the income funds is $1100. For the growth‑oriented funds the mean increase is $1090.

At the 0.01 significance level is there a difference in the mean yield of the two funds? Assume that σ₁ = $45 and σ₂ = $55. State your work in the 5-step hypothesis test.

Answer 1

Answer

a. null and alternative hypothesis.
We have two samples with mean information so we use a 2-sample Z-Test.
Ho: u1-u2 = 0
H1: u1-u2 is not equal to zero
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b. state the decision rule.
If the test statistic is lee than -2.576 or greater than 2.576, reject Ho.

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c. compute the value of the test statistic
z(1100-1090) = (1100-1090)/sqrt[(45^2/35) + (55^2/40) = 0.8655
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d. Compute the p-value.
p-value = 2*P(z > 0.8655)) = 2* = 38.68%
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e. state the decision of the null hypothesis
Conclusion: Since p-value is greater than 1%, Fail to reject Ho.