A lawn mower-manufacturing company would like to advertise that their top of the

Question

A lawn mower-manufacturing company would like to advertise that their top of the line self-propelled mower can go 250 hours before experiencing starting problems (more than 2 pulls) and subsequent service. During year-round field tests of 10 identical lawn mowers at a proving ground in a warm climate, the lawn mowers required service 205, 430, 301, 199, 222, 124, 89, 289, 260, and 214 hours. Based on this data, can the manufacturer make this advertising claim? Explain clearly how you came to your decision.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   250  
Ha:    u   <   250  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    233.3          
uo = hypothesized mean =    250          
n = sample size =    10          
s = standard deviation =    95.64755907          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.55213157          
              
Also, the p value is              
              
p =    0.290429107          
              
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Hence, there is no significant evidence to show that the manufacturer's claim is false at 0.05 level. Hence, his claim stands.      

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