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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

Solution

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]