Question 233173: I submitted this question already and there was no solution to this problem.
Consider the sample data below. 34
21
23
52
34
38
36
49
36
34
20
50
44
36
43
27
45
40
52
39
31
54
20
30
34
50
40
25
26
27
26
21
43
Suppose we wish to test the following hypotheses for the data:
Ho:u < 40
Ho: u > 40
Given the mean and the standard deviation of the data as above:
(A) Compute the appropriate test statistic for testing (show all work).
(B) Determine the critical value for α = 0.05.
(C) Test Ho using the traditional/classical method.
(D) State the decision based on the results of the test.
(E) Had you used the p-value method of hypothesis testing, what would the p-value have been?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose we wish to test the following hypotheses for the data:
Ho:u <= 40
Ho: u > 40
------------------------------------------------
Given the mean and the standard deviation of the data as above:
sample mean = 36 ; sample std = 10.3923
------------------------------------------------
(A) Compute the appropriate test statistic for testing (show all work).
ts = z(36) = (36-40)/[10.3923/sqrt(30)] = -2.108..
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(B) Determine the critical value for alpha = 0.05.
For one-tail test with alpha=5% and df=29: cv = -1.699..
=====================
(C) Test Ho using the traditional/classical method.
Reject Ho because the test statistic is in the rejection
interval (-inf,-1.699..)
=======================
(D) State the decision based on the results of the test.
u < 40
=======================
(E) Had you used the p-value method of hypothesis testing, what would the p-value have been?
p-value is P(t < -2.108, with df=29) = tcdp(-100,-2.108,29) = 0.0219..
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Cheers,
Stan H.
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