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 = $585 million. The standard deviation of the amount managed by advisers from Company B was s2 = $481 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. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion. Do not reject Ho. We cannot conclude there is a statistically significant difference between the variances for the two companies. O Reject Ho. We cannot conclude there is a statistically significant difference between the variances for the two companies. Reject Ho, we can conclude there is a statistically significant difference between the variances for the two companies. Do not reject Ho- We can conclude there is a statistically significant difference between the variances for the tompanies.

Answer 1

To test $H_0: \sigma_1^2 = \sigma_2^2$ against $H_1: \sigma_1^2 \neq \sigma_2^2$

Here

$s_1 = 585,n_1 = 16,s_2 = 481,n_2 = 10$

The test statistic can be written as

$F = \frac{s_1^2}{s_2^2}$ which under H₀ follows a F distribution with $(n_1-1,n_2-1)$ df.

We reject H₀ at 10% level of significance if P-value < 0.10

Now,

The value of the test statistic $F_{obs} = 1.47918$

and P-value $=P(F_{n_1-1,n_2-1}>F_{obs} )=P(F_{15,9} >1.47918) = 1 - 0.719187 = 0.280813$

Since P-value > 0.10, so we fail to reject H₀ at 10% level of significance and we cannot conclude that there is a statistically significant difference between the variances for the two companies.

ans->i)