Question 1039390
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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 <font color=blue>"you are only concerned if the actual costs are higher than the $30,000 target"</font>


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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 <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">table</a>. 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 <font color=red>red</font>


<font color=red>The tp is 1.341</font>
The tp is 0.866 
The tc is 11.429 
<font color=red>The tc is 2.286 </font>
<font color=red>We would reject the null hypothesis </font>
We would fail to reject the null hypothesis 
We would conclude that it is reasonable to use the $30,000 budget figure 
<font color=red>We would recommend revising the budget figure </font>


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