Question 187926: 1. To reduce operating costs, First UP Bank wants to make sure that the loan department in its branches manage the number of courier packages sent out to appraisers etc. to 15 or less every week. The Bank examined the loan departments of 25 randomly chosen branches and the results show that an average of 14.2 packages with a standard deviation of 2.2 packages were sent during one week in late February. These numbers were fed into the Megastat Add-in in Excel and yield the following output:
Hypothesis Test: Mean vs. Hypothesized Value
15.000 hypothesized value
14.200 mean Packages
2.200 std. dev.
0.440 std. error
25 n
24 df
-1.82 t
.0408 p-value (one-tailed, lower)
At the 0.1 level of significance, is the true average number of packages less than 15? Please state the null and alternative hypothesis as well as the decision rule that you use to arrive at the conclusion.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. To reduce operating costs, First UP Bank wants to make sure that the loan department in its branches manage the number of courier packages sent out to appraisers etc. to 15 or less every week.
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Ho: u <= 15
Ha: u > 15
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The Bank examined the loan departments of 25 randomly chosen branches and the results show that an average of 14.2 packages with a standard deviation of 2.2 packages were sent during one week in late February. These numbers were fed into the Megastat Add-in in Excel and yield the following output:
Hypothesis Test: Mean vs. Hypothesized Value
15.000 hypothesized value
14.200 mean Packages
2.200 std. dev.
0.440 std. error
25 n
24 df
-1.82 t
Note: The test statistic should be t(14.2) = (14.2-15)/[2.2/sqrt(25)] = -1.82
p-value should be P(t > -1.82 with df = 24) = 0.9594
The p-value has a lower tail of .0408
At the 0.1 level of significance, is the true average number of packages less than 15?
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Decision Rule for right-tail test with alpha = 1% and alpha = 24
Reject Ho if t > 2.492
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Conclusion:
The number sent is less than or equal to 15 because we Fail to reject Ho
because the p-value is greater than 1%.
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Comment: The narrative describing the claim implies Ha is u>15.
But the data below the narrative leans in the direction of a
left-tail test. Confusing.
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Cheers,
Stan H.
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