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ID: 3394654 • Letter: H
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home / study / questions and answers / math / statistics and probability / a sample of 37 observations is selected from a ... Question A sample of 37 observations is selected from a normal population. The sample mean is 25, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level. H0 : ? ? 24 H1 : ? > 24 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? Comment
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 24
Ha: u > 24
As we can see, this is a right tailed test. [ONE TAILED TEST]
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b)
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Thus, reject Ho when z > 1.64485. [ANSWER]
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c)
Getting the test statistic, as
X = sample mean = 25
uo = hypothesized mean = 24
n = sample size = 37
s = standard deviation = 5
Thus, z = (X - uo) * sqrt(n) / s = 1.216552506 [ANSWER]
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d)
As z < 1.64485, we FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER]
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e)
Also, the right tailed p value is
p = 0.111887261 [ANSWER]
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
There is no significant evidnece that the true mean is greater than 24. [CONCLUSION]
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