Consider a paint-drying situation in which drying time for a test specimen is no

Question

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 9. The hypotheses H0: = 74 and Ha: < 74 are to be tested using a random sample of n = 25 observations.

0.002, what is (70)? (Round your answer to four decimal places.) (c) For the test procedure with (70) = 0.2303 (d) If the test procedure with -0.002 is used, what n is necessary to ensure that (70) 0.017(Round your answer up to the next whole number.) n 135 specimens n = 135 (e) If a level 0.01 test is used with n - 100, what is the probability of a type I error when (e) If a level 0.01 test is used with n = 100, what is the probability of a type 1 error when = 767 (Round your answer to four decimal places.) 76? (Round your answer to four decimal places.) 0.0099

Explanation / Answer

c)

P(Z < x-74/9/sqrt(25)) = 0.002

=>

x -74 /9/sqrt(25) = invnorm(0.002)

=>

x = 68.82

B(70) = P(Z > 68.82 - 70/9/sqrt(25))

= P(Z > -0.6555)

= 0.7440

d)

B(70) = 0.01

=>

P(z > 68.82 - 70/9/sqrt(n)) =0.01

68.82 - 70/9/sqrt(n) = -2.3264

=>

n =315

e)

P( type 1 error)

= P(Z < 76-74/9/10)

= P(Z < 2.22)

= 0.9869

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