SOLUTION: Has the cost to outsource a standard employee background check changed from 2005 to 2006? A random sample of 10 companies in spring 2005 showed a sample average of $105 with a samp

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Question 146065: Has the cost to outsource a standard employee background check changed from 2005 to 2006? A random sample of 10 companies in spring 2005 showed a sample average of $105 with a sample standard deviation equal to $32. A random sample of 10 different companies in spring 2006 resulted in a sample average of $75 with a sample standard deviation equal to $45. (a) Conduct a hypothesis test to test the difference in sample means with a level of significance equal to .05. Assume the population variances are not equal. (b) Discuss why a paired sample design might have made more sense in this case.
Answer by stanbon(75887) (Show Source):
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Has the cost to outsource a standard employee background check changed from 2005 to 2006? A random sample of 10 companies in spring 2005 showed a sample average of $105 with a sample standard deviation equal to $32. A random sample of 10 different companies in spring 2006 resulted in a sample average of $75 with a sample standard deviation equal to $45.
(a) Conduct a hypothesis test to test the difference in sample means with a level of significance equal to .05. Assume the population variances are not equal.
Ho: means are the same
Ha: means are not the same
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I ran a 2-Sample T-test on a TI calculator and got the following:
t = 1.7181
p-value = 0.1047
Conclusion: Since p-value is greater than 5%, fail to reject Ho.
The means are statistically the same.
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(b) Discuss why a paired sample design might have made more sense in this case.
It wouldn't because the two samples are independent.
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Cheers,
Stan H.