A company makes high-definition televisions and does not like to have defective pixels. Historically, the mean number of defective pixels in a TV is 20. An engineer is hired to make better TV’s that have fewer defective pixels. After his first week of work he claims that he can significantly improve the current method. To check his claim you try his new method on 100 new televisions. The average number of defective pixels in those 100 TV’s is 19.1. Assume that the new method doesn’t change the standard deviation of defective pixels, which has always been 4. (a) Test if the new method is significantly better than the old one at the α = 0.05 level. (b) Using the new method, assume that the mean number of defective pixels is actually 19. What is the chance that your test from part 1 will conclude that the new method is statistically more effective?
A company makes high-definition televisions and does not like to have defective pixels. Historically,
the mean number of defective pixels in a TV is 20. An engineer is hired to make better TV’s that have
fewer defective pixels. After his first week of work he claims that he can significantly improve the current
method. To check his claim you try his new method on 100 new televisions. The average number of
defective pixels in those 100 TV’s is 19.1. Assume that the new method doesn’t change the standard
deviation of defective pixels, which has always been 4.
(a) Test if the new method is significantly better than the old one at the α = 0.05 level.
(b) Using the new method, assume that the mean number of defective pixels is actually 19. What is the
chance that your test from part 1 will conclude that the new method is statistically more effective?
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