Consider a paintdrying situation in which drying time for a

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 8. The hypotheses H₀: = 74 and H_a: < 74 are to be tested using a random sample of n = 25 observations.

If a level 0.01 test is used with n = 100, what is the probability of a type I error when = 76? (Round your answer to four decimal places.)

Solution

For alevel of 0.01, with n = 100, we findthe Type I errorwhen U = 76.
a= P(X <74 when U=76)
= P(74-76/(8/Sqrt(100))
= P ( Z <-2.5) From Standard Normal Table
= 0.0062