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t test for independent samples assuming equal variance

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Any conclusion drawn for the t-test statistical process is only as good as the research question asked and the null hypothesis formulated. T-tests are only used for two sample groups, either on a pre post-test basis or between two samples (independent or dependent). The t-test is optimized to deal with small sample numbers which is often the case with managers in any business. When samples are excessively large the t test becomes difficult to manage due to the mathematical calculations involved.

Using the raw measurement data presented above, determine whether or not there exists a statistically significant difference between the salaries of female and male human resource managers using the appropriate t-test. Draw the appropriate conclusions with respect to female and male HR salary levels. Report the required "t" critical values based on the degrees of freedom.

Salary Level
Female HR Directors Male HR Directors
$50,000 $58,000
$75,000 $69,000
$72,000 $73,000
$67,000 $67,000
$54,000 $55,000
$58,000 $63,000
$52,000 $53,000
$68,000 $70,000
$71,000 $69,000
$55,000 $60,000

*Do not forget what we all learned in high school about "0"s

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Solution Summary

The solution provides detailed information how to conduct the t test for independent samples assuming equal variance.

Solution Preview

First, we perform the F test to check if we could assume there is equal variance between the two groups.

The critical F value F=FINV(0.05,9,9)=3.18
The ...

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