A manufacturer that produces display panels used in digital cameras has announce

Question

A manufacturer that produces display panels used in digital cameras has announced the release of a new 3-inch, high-definition LCD display panel. He claims that the average lifetime of the new panel is about 10,000 hours. To support his claim, a sample of 26 display panels is randomly selected from the production line and the corresponding average lifetime is 11,520 hours with a standard deviation of 2,800 hours. The distribution of the lifetime is known to be normally distributed.

a At the 0.02 level of significance, is there any evidence to reveal that the average lifetime of the new panel is 10,000 hours?

      b Use the p-value approach to test the hypothesis at the same level of significance.

c With reference to the result of the hypothesis test obtained in part (a) above, which kind of error (Type I or Type II) is not plausible to be committed? Justify your answer.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   10000  
Ha:    u   =/   10000  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    25          
tcrit =    +/-   2.485107175      
              
Getting the test statistic, as              
              
X = sample mean =    11520          
uo = hypothesized mean =    10000          
n = sample size =    26          
s = standard deviation =    2800          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.768039165          
              
As |t| > 2.485, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that the mean lifetime of the new panel is not 10000 hours at 0.02 level. [CONCLUSION]

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b)

Also, the p value is, as this is two tailed,              
              
p =    0.010464219          
              
As P < 0.02, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that the mean lifetime of the new panel is not 10000 hours at 0.02 level. [CONCLUSION]
  
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c)

As we rejected Ho, then we ar at risk of a TYPE I ERROR. [ANSWER]

[Note: Type I error is incorrectly rejecting Ho.]

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