Question

The partners at an investment firm want to know which of their two star financial planners, Brayden or Zoe, produced a higher mean rate of return last quarter for their clients. The partners reviewed last quarter’s rates of return for random samples of clients who were managed by Brayden or Zoe. The mean rate of return for the sample of 30 of Brayden’s clients was 3.54% with a standard deviation of 0.92%. The mean rate of return for a sample of 30 of Zoe’s clients was 3.87% with a standard deviation of 2.08%. Let μ1 be the population mean rate of return for Brayden’s clients and μ2 be the population rate of return for Zoe’s clients. The partners assume the population standard deviations are not equal and, since Zoe's mean is higher, test the alternative hypothesis Ha:μ1−μ2<0. If the p-value of the hypothesis test is greater than 0.10 and the significance level is α=0.05, what conclusion could be made about the population mean rate of return for Brayden and Zoe? Identify all of the appropriate conclusions to the hypothesis test below.
Select all that apply:
A. Reject the null hypothesis
B. Fail to refect the null hypothesis
C. The conclusion of the hypothesis tests is that there is sufficient evidence to suggest that the population mean rate of return for Zoe is greater than the population mean rate of return for Brayden.
D.The conclusion of the hypothesis tests is that there is insufficient evidence to suggest that the population mean rate of return for Zoe is greater than the population mean rate of return for Brayden.

Answer 1

Answer:

Correct options are (B) and (C).

Step-by-step explanation:

A two-sample t-test can be used to determine which of the two star financial planners, Brayden or Zoe, produced a higher mean rate of return last quarter for their clients.

The hypothesis is defined as:

H₀: The population mean rate of return for Brayden is same as that for Zoe, i.e. μ₁ - μ₂ = 0.

Hₐ: The population mean rate of return for Brayden is less than that for Zoe, i.e. μ₁ - μ₂ < 0.

The significance level of the test is, α = 0.05.

The decision rule is:

If the p-value of the test is less than the significance level of 5% then the null hypothesis is rejected.

And if the p-value of the test is more than the significance level of 5% then the null hypothesis is failed to be rejected.

The p-value of the test is computed to:

p-value > 0.10

If the p-value is greater than 0.10 then it is definitely greater than 0.05.

So, p-value > α = 0.05.

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The conclusion of the hypothesis tests is that there is sufficient evidence to suggest that the population mean rate of return for Zoe is greater than the population mean rate of return for Brayden.

Thus, the correct options are (B) and (C).