Question 138699
A sample of 36 observations is selected from a normal population. The sample mean is 21, and the sample standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level. 
H0: µ ≥ 20 
H1: µ < 20 
Answer the Questions: 
(a) Is this a one or two tailed test? 
H1 tells you it is a one-tailed test.  Hi always tells you 
if you have a one tail(< or >) or two tail (not equal to) test.
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(b) What is the decision rule?
t value for one-tail test with alpha = 5% and df=35 is 1.645
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(c) What is the value of the test statistic?
t(21) = (21-20)/[5/sqrt(36)] = 6/5 = 1.2
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(d) What is your decision regarding H0? 
Since the test statistic is not in the reject interval, Fail to reject Ho.
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(e) What is the p-value? Interpret it.
p-value = P(1.2 < z < 10) = 0.1151
Interpretation: 11.51% of test results could have provided stronger
evidence for rejecting Ho.
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Cheers,
Stan H.