Question 138699: Please help with this problem. Don't know which text the intructor got it from. Thank you!!
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? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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