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 = $488 million. Conduct a hypothesis test at ? = 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. H0: ?12 ≠ ?22 Ha: ?12 = ?22 H0: ?12 ≤ ?22 Ha: ?12 > ?22 H0: ?12 = ?22 Ha: ?12 ≠ ?22 H0: ?12 > ?22 Ha: ?12 ≤ ?22 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. Reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies. Do not reject H0. We can conclude there is a statistically significant difference between the variances for the two companies. Do not reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies. Reject H0. We can conclude there is a statistically significant difference between the variances for the two companies.
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 = $488 million. Conduct a hypothesis test at ? = 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. H0: ?12 ≠ ?22 Ha: ?12 = ?22 H0: ?12 ≤ ?22 Ha: ?12 > ?22 H0: ?12 = ?22 Ha: ?12 ≠ ?22 H0: ?12 > ?22 Ha: ?12 ≤ ?22 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. Reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies. Do not reject H0. We can conclude there is a statistically significant difference between the variances for the two companies. Do not reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies. Reject H0. We can conclude there is a statistically significant difference between the variances for the two companies.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 = $488 million.
Conduct a hypothesis test at
? = 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.
H0: ?12 ≠ ?22
Ha: ?12 = ?22
H0: ?12 ≤ ?22
Ha: ?12 > ?22
H0: ?12 = ?22
Ha: ?12 ≠ ?22
H0: ?12 > ?22
Ha: ?12 ≤ ?22
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.
Reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies.
Do not reject H0. We can conclude there is a statistically significant difference between the variances for the two companies.
Do not reject H0. We cannot conclude there is a statistically significant difference between the variances for the two companies.
Reject H0. We can conclude there is a statistically significant difference between the variances for the two companies.
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