Question 588398
a)

Hypothesis:


Ho: mu = 24

Ha: mu =/= 24


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Critical T-value (for t-distribution with df = 8-1 = 7) is t = 2.365

Note: use alpha/2 = 0.05/2 = 0.025

You can find the Inverse T-Distribution Table here:
<a href="http://www.zweigmedia.com/RealWorld/finitetopic1/t_table.html">http://www.zweigmedia.com/RealWorld/finitetopic1/t_table.html</a>


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Test Statistic:


For this, we need the mean xbar and the sample standard deviation s. We can find both with a calculator to get xbar = 25 and s = 1.1952286 


t = (xbar - mu)/(s/sqrt(n))


t = (25 - 24)/(1.1952286/sqrt(8))


t = 2.3664319



Since the test statistic (2.3664319) is greater than the critical t-value (2.365), this means that the test statistic lies in the rejection region.


So this tells us to reject the null hypothesis.


So this allows us to conclude that the mean number of hours differs significantly from 24.


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b)


The distribution involved is the t-distribution with 7 degrees of freedom and it's shown below


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/t_distribution.png">


I've also included the rejection region, the critical values and the test statistic. You can see that the test statistic lies in the red rejection region.



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c)


Essentially, the distribution shown in part B is the set of all possible cycles (we're assuming it is anyway). The values in the red regions are values that are very unlikely (at a significance level of 5%). So if you find any values in these regions, then it's unlikely that the assumed distribution is true.