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.

Hope can answered by expert “Shanmugham”, or other experts as him could answer completely of above a, b, c questions clearly.

Explanation / Answer

a)the distribution is given to be normal therefore we will use the z table

the null hypothesis = H0=u=10000

the alternate hypothesis = Ha= u >10000

the alpha = 0.02

we will get the z score = (11520 - 10000)/(2800/sqrt(26))

= 2.76

b) as the z score is 2.76

therefore from the z table the p value = 0.9971

which is bigger then the 0.02 there fore we will accept the null hypothesis

c) in this as the null hypothesis is true therefore only type 1 error can take place which occur when we reject the true null hypothesis.

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