A sample of 48 observations is selected from a normal popula

A sample of 48 observations is selected from a normal population. The sample mean is 57, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.01 significance level.

H0: = 58 H1: 58

A.is this a one-tail or two-tail test

B.What is the decision rule?

C.What is the value of the test statistic?

D. What is your decision regarding H₀? Reject or fail to reject

E. what is the p-value?

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   58  
Ha:    u   =/   58  
              
As we can see, this is a TWO tailed test, as Ha used =/=. [ANSWER, TWO TAILED]      

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b)
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      

Thus, reject Ho when z < -2.576 or z > 2.576. [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    57          
uo = hypothesized mean =    58          
n = sample size =    48          
s = standard deviation =    6          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.154700538 [ANSWER]

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d)

As -2.576<z<2.576, we FAIL TO REJECT HO. [ANSWER]

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e)

Also, the p value is, as this is two tailed,              
              
p =    0.248213079   [ANSWER]