Question

Barron's has collected data on the top 1,000 financial advisers. Company A and Company B have many of their advisers on this list. A sample of 16 of the Company A advisers and 10 of the Company B advisers 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 the Company A advisers was s1 = $583 million. The standard deviation of the amount managed by the Company B advisers was s2 = $489 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? State the null and alternative hypotheses.

Answer 1

Answer:

We'll start by putting into consideration, the large sample variance at the numerator.

Barron's Variance will be represented using 1 as the subscript.

i.e.

1 = $583 million

2 = $489 million

So,

0: 1²= 2²

: 1² ≠ 2²

=1² / 2²=

= $583 million² / $489 million²

= 583²/489²

= 1.42

Degrees of freedom 15 and 9

Using F table, area in tail is greater than 0.10.

Two-tail p-value is greater than .20

Exact p-value corresponding to F= 1.42 is .5874 (See F table)

p-value > .10

So,we do not reject 0.

We cannot conclude there is a statistically significant difference between the variances for the two companies.