Question 171574
6) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that ! is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees 
weights is less than 200 lb. 
Ho: mu >= 200
Ha: mu < 200
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n= 54; s = 121.2, x-bar = 183.9, alpha = 0.10
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If you use a z-test you get:
test statistic = -0.97516.. and p-value=0.164493...
Conclusion: Since p>10%, Fail to reject Ho.
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If you use a t-test you get:
test statistic = -0.976158... and p-value = 0.1667104
so you would still "Fail to Reject Ho".
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Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. 
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7) A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-&#64257;ve job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of signi&#64257;cance to test the claim that this sample comes from a population with a mean score greater than 160. 
Ho: u = 160
Ha: u > 160
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n=25; sample mean = 183, s=12, alpha = 5%
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z-test results: test statistic = 9.583333... p-value = 1.0000
since p is greater than 5%, Fail to reject Ho.
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t-test results: test stat= 9.58333; p-value = 0.9999999
Conclusion: same as z-test
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Comment: I have a feeling that your posted data for the 2nd
question is not accurate. Is that standard deviation really 12?
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Cheers,
Stan H.