Question

Data were collected on the top 1,000 financial advisers. Company A had 239 people on the list and another company, Company B, had 121 people on the list. A sample of 16 of the advisers from Company A and 10 of the advisers from Company B showed that the advisers managed many very large accounts with a large variance in the total amount of funds managed. The standard deviation of the amount managed by advisers from Company A was s1 = $589 million. The standard deviation of the amount managed by advisers from Company B was s2 = $488 million. Conduct a hypothesis test at α = 0.10 to determine if there is a significant difference in the population variances for the amounts managed by the two companies. What is your conclusion about the variability in the amount of funds managed by advisers from the two firms?

Answer 1

Kindly check explanation

Explanation:

Company A:

Number of people = 239

Number of sample (n) = 16

Standard deviation (s1) = 589 million

Company B:

Number of people = 121

Number of sample(n) = 10

Standard deviation (s2) = 488 million

We can find the F - statistic:

Fstat = variance 1 / variance 2

Variance = (standard deviation)²

Fstat = 589² / 488²

Fstat = 346921 / 238144

Fstat = 1.4567698 = 1.46

Degree of freedom:

Sample A : (n - 1) = (16 - 1) = 15

Sample B: (n - 1) = (10 - 1) = 9

USing the P-value from F statistic calculator at df(15,9) ; Fstat= 1.46

P value = 0.287797.

Since the p value is > 0.10, then result is not significant, hence we fail to reject the null hypothesis.