Question 1039390: 2) The program office budgets $30,000 per program review at the contractor’s site. Your concern for “end of year” spending drills is that you have budgeted enough for the reviews (i.e. you are only concerned if the actual costs are higher than the $30,000 target). A sample of 16 trips yielded a mean of $32,000 and a standard deviation of $3,500. Test the budgeted amount at the 80% level of confidence. Select the correct answer out of each pair of choices. (Carry intermediate calculations to three decimal places.)
The tp is 1.341
The tp is 0.866
The tc is 11.429
The tc is 2.286
We would reject the null hypothesis
We would fail to reject the null hypothesis
We would conclude that it is reasonable to use the $30,000 budget figure
We would recommend revising the budget figure
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Hypothesis
Null:
H0: mu = 30,000
Alternate
H1: mu > 30,000
This is a one-tailed test to the right. Ie, a right-tailed test. We reject the null (H0) if the test statistic is larger than the critical value.
This is a right-tailed test because of the phrasing "you are only concerned if the actual costs are higher than the $30,000 target"
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Test statistic:
T = (xbar - mu)/(sigma/sqrt(n))
T = (32000-30000)/(3500/sqrt(16))
T = 2.28571428571429
T = 2.286
So the test statistic is approximately 2.286
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Critical Value:
Use a table. Tables such as these are often found at the back of your statistics textbook.
Look at the confidence level of 80%. Highlight the entire column with the 80% confidence level. Also, highlight the row that starts with df = 15 (note: n = 16 is our sample size, so the degrees of freedom is df = n-1 = 16-1 = 15). The value at this row and column is 1.341
So the t critical value is 1.341.
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Since the test statistic (2.286) is larger than the t critical value (1.341), this means that we reject the null hypothesis. So we conclude that the alternate hypothesis is correct. In other words, the budget should be revised because it's very possible that the budget should be increased.
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Summary:
Answers are highlighted in red
The tp is 1.341
The tp is 0.866
The tc is 11.429
The tc is 2.286
We would reject the null hypothesis
We would fail to reject the null hypothesis
We would conclude that it is reasonable to use the $30,000 budget figure
We would recommend revising the budget figure
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