Bjork Larsen was trying to decide whether to use a new racin

Bjork Larsen was trying to decide whether to use a new racing wax for cross country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to test the wax by racing on the course 9 times. His 8 race times were 58.2, 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds. Should he buy the wax? Justify your answer using appropriate t or z -test. Show process of hypothesis testing and test using 0.01 level of significance.

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   55  
Ha:    u   <   55  
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B)
              
As we can see, this is a    left   tailed test.      
              
Getting the test statistic, as              
              
X = sample mean =    53.66666667          
uo = hypothesized mean =    55          
n = sample size =    9          
s = standard deviation =    6.790802604          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.589031994 [ANSWER]

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c)          

Thus, getting the critical t,              
df = n - 1 =    8          
tcrit =    -   2.896459448   [ANSWER]

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d)

Reject Ho when t < -2.896 [ANSWER]

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e)

As t is not less than -2.896, then we FAIL TO REJECT HO.

There is no significant evidence that the average is less than 55 s, so he shouldn\'t buy it.              
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Also, the p value is              
              
p =    0.286046498   [ANSWER]