Question

The partners at an investment firm want to determine which of two financial planners produced a higher population mean rate of return for their clients. The partners reviewed the rates of return last quarter for random samples of the clients. For one of the planners, the sample mean rate of return for the 25 clients selected was 3.0% with a sample standard deviation of 0.8%. For the other planner, the sample mean rate of return for the 25 clients selected was 3.4% with a sample standard deviation of 2.0%. Determine the number of degrees of freedom for a two-mean hypothesis test for population variances assumed not equal (nonpooled estimate of the standard deviation) to test whether one planner produced a higher population mean rate of return.

A) 48

B) 49

C) 50

D) 51

Answer 1

The degrees of freedom for the two-mean hypothesis test in question, calculated using the Welch-Satterthwaite equation based on the provided sample sizes and variances, is approximately 27.11, which would be rounded down to 27. None of the given answer choices match this calculated value.

Step-by-step explanation:

To determine the number of degrees of freedom for a two-mean hypothesis test when population variances are assumed not to be equal (nonpooled estimate), we use the following formula based on the sample sizes and sample standard deviations:

n1 = 25, s1 = 0.8%
n2 = 25, s2 = 2.0%

The degrees of freedom (df) can be approximated using the Welch-Satterthwaite equation:

df ≈ ( (s1^2/n1 + s2^2/n2)^2 ) / ( (s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1) )

Upon calculation, you will get df ≈ 27.11, which, when rounded down to the nearest whole number, gives you 27 degrees of freedom. Since the provided answer choices do not have this option, we cannot accurately select one of the provided choices A) 48, B) 49, C) 50, or D) 51.