Examine the following hypothesis test with n10 overbar x 671

Examine the following hypothesis test with

n=10, overbar x =67.1, s=9.7, and =0.005.

H0:

65

HA:

>

65

a. State the decision rule in terms of the critical value of the test statistic.

b. State the calculated value of the test statistic.

(CORRECT ANSER GIVEN IS .685 PLEASE EXPLAIN HOW TO COMPLETE)

c. State the conclusion.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   65  
Ha:    u   >   65  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    +   3.249835542      

Thus, we reject the null hypothesis if t > 3.25. [ANSWER, PART A]

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B)

Getting the test statistic, as              
              
X = sample mean =    67.1          
uo = hypothesized mean =    65          
n = sample size =    10          
s = standard deviation =    9.7          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.684616813 [ANSWER, TEST STATISTIC]          

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c)              
              
Comparing t < 3.25, we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the mean is greater than 65. [CONCLUSION]