(21 marks) An LCD display manufacturer has announced the release of a new LED 32
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Question
(21 marks)
An LCD display manufacturer has announced the release of a new LED 32-inch display panel. The production manager of the company claims that the average lifetime of the panel is longer than 16,000 hours. To support his claim, a random sample of 25 display panels of the same model is randomly selected from the production line and the corresponding average lifetime is 16,400 hours with a standard deviation of 2,000 hours. The distribution of the lifetime is known to be normally distributed.
a) At the 0.05 level of significance, is there any evidence to reveal that the average lifetime of the new panel is longer than 16,000 hours? (10 marks)
b) Use the p-value approach to test the hypothesis at the same level of significance. (5 marks)
c) With reference to the result of the hypothesis test obtained in part (a) above, which kind of error (Type I or Type II) could possibly be committed? Justify your answer. (6 marks)
Explanation / Answer
n = 25
xbar = 16400
std.dev. = 2000
a)
Below are the null and alternate hypo
H0: mu = 16000
H1: mu > 16000
test statistics, t = (16400 - 16000)/(2000/sqrt(25)) = 1
p-value = 0.1587
b)
As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
c)
Possible error is Type II error i.e. incorrectly fail to reject the null hypothesis.
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