The following information applies to the questions displayed

[The following information applies to the questions displayed below.]

The sample mean is 60, and the sample size is 37. The population standard deviation is 8.

1.

Required information

Two-tailed test

One-tailed test

2.

Required information

Reject H₀ if -1.65 < z < 1.65

Reject H₀ if z < -1.65 or z > 1.65

3.

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What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4.

Required information

Reject H₀

Fail to reject H₀

5.

Required information

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   61  
Ha:    u   =/   61  

As Ha uses =/, then it is TWO TAILED TEST. [ANSWER]

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2.

              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha/2 =    0.05          
zcrit =    +/-   1.644853627      

Thus, we reject Ho if z < -1.65 or z > 1.65. [ANSWER]

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3.
              
Getting the test statistic, as              
              
X = sample mean =    60          
uo = hypothesized mean =    61          
n = sample size =    37          
s = standard deviation =    8          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.760345316 = -0.76 [ANSWER]          
  
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4.

As |z| < 1.65, then we FAIL TO REJECT HO. [ANSWER]

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5.          

Also, the p value is, as this is two tailed,              
              
p =    0.4472 [ANSWER]