It was reported that a certain population had an average of 27. To test this cla

Question

It was reported that a certain population had an average of 27. To test this claim, you selected a random sample of 150. The computed sample average was 25 and the sample SD was 7. The null and alternative hypotheses are H_o: The average of the population = 27 H_A: The average of the population notequalto 27 Find the test statistic for this test. Z-statistic t-statistic Confidence Interval chi^2-statistic Find the p-value for this test. 0.050 0.001 0.00015 0.000467 What is the conclusion (reject or do not reject) and what does it mean? Accept H_0 Reject H_0 and Accept H_A

Explanation / Answer

a)

As n = 150, it is large enough to use

OPTION A: Z STATISTIC [ANSWER]

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   27  
Ha:    u   =/   27  
              
As we can see, this is a    two   tailed test.      
              
Getting the test statistic, as              
              
X = sample mean =    25          
uo = hypothesized mean =    27          
n = sample size =    150          
s = standard deviation =    7          
              
Thus, z = (X - uo) * sqrt(n) / s =    -3.499271061 [ANSWER, TEST STATISTIC]          

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b)

              
Also, the p value is, as this is two tailed,              
              
p =    0.000467 [ANSWER, D]      

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C)
              
As this is a small P value, we   REJECT THE NULL HYPOTHESIS.   [OPTION B]      

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