Consider the following hypothesis test H0 25 Ha 25 A sample

Consider the following hypothesis test:

H0: 25
Ha: > 25

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. At  = .01, what is your conclusion?

p-value -

d. What is the rejection rule using the critical value?

Reject H0 if z -

What is your conclusion?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   25  
Ha:    u   >   25  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    26.4          
uo = hypothesized mean =    25          
n = sample size =    40          
s = standard deviation =    6          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.475729575 [ANSWER, TEST STATISTIC]

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B)

Also, the p value is              
              
p =    0.070008252   [ANSWER, P VALUE]

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c)

As P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.

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d)

Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          

zcrit =    +2.326347874      

So, we reject Ho if z > 2.3263. [ANSWER]

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As z < 2.3263, we FAIL TO REJECT THE NULL HYPOTHESIS.

There is no significant evidence that the mean is greater than 25. [CONCLUSION]