Question

This question involves the 2-SampleFTest test for comparing two unknown population variances (or SD’s) and the ANOVA test

include:

1. Clear statement of hypotheses, with the correct parameter(s)
2. An indication of the test used
3. The test statistic and p-value
4. An indication of the statistical decision (i.e. whether or not to reject Ho)
     along with an explanation.
5. An interpretation of the statistical decision in the context of the problem.

The annual salaries for a random sample of 16 actuaries working in New York have a standard deviation of $16,000.   The annual salaries of a random sample of 17 actuaries working in California have a standard deviation of $9600.   Using a significance level of a = .05, is there significant evidence that the standard deviation of the annual salaries is greater in New York than it is in California?  

Answer 1

Result:

This question involves the 2-SampleFTest test for comparing two unknown population variances (or SD’s) and the ANOVA test

The annual salaries for a random sample of 16 actuaries working in New York have a standard deviation of $16,000.   The annual salaries of a random sample of 17 actuaries working in California have a standard deviation of $9600.   Using a significance level of a = .05, is there significant evidence that the standard deviation of the annual salaries is greater in New York than it is in California?  

1. Clear statement of hypotheses, with the correct parameter(s)

Test whether the standard deviation of the annual salaries is greater in New York than it is in California.

Parameter: population standard deviation

Upper tail test.

2. An indication of the test used
F test for comparing two variances used

3. The test statistic and p-value

F Test for Differences in Two Variances
Data
Level of Significance	0.05
Larger-Variance Sample
Sample Size	16
Sample Variance	256000000
Smaller-Variance Sample
Sample Size	17
Sample Variance	92160000
Intermediate Calculations
F Test Statistic	2.7778
Population 1 Sample Degrees of Freedom	15
Population 2 Sample Degrees of Freedom	16
Upper-Tail Test
Upper Critical Value	2.3522
p-Value	0.0254
Reject the null hypothesis

Test value = 2.7778

P value = 0.0254

4. An indication of the statistical decision (i.e. whether or not to reject Ho)
     along with an explanation.

Calculated p value 0.0254 < 0.05 level of significance.

Ho is rejected.

5. An interpretation of the statistical decision in the context of the problem.

There is sufficient evidence that the standard deviation of the annual salaries is greater in New York than it is in California.