Stats Help A company that manufactures light bulbs has adver

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A company that manufactures light bulbs has advertised that its 75-watt bulbs burn an average of 800 hours before failing. In reaction to the company\'s advertising campaignb, several dissatisfied customers have complained to a consumer watchdog organization that they believe the compan\'s clam to be exaggerated. The consumer organization must decide whther or not to allocaate some of its financtial resources to countering the compan\'y advertising campaign. So that it can make an informed dicision, it befins by purchasing and testing 100 of the disputed light bulbs. In this experiment, the 100 light bulbs burned an average of x =745.1 hours before failing, with a sample standard deviation of s=238.0 hours. Formulate null and alternative hypotheses that are appropriate for this situation. Calcuate a significance probability. Do these results warrant rejecting the null hypothesis at a significnace level of =0.05?

Thank you!

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   800  
Ha:    u   <   800  
              
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 =    745.1          
uo = hypothesized mean =    800          
n = sample size =    100          
s = standard deviation =    238          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.306722689          
              
As z < -1.645, then we reject the null hypothesis.

Thus, there is significant evidence that the mean is less than 800 hours. [CONCLUSION]