Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 7. The hypotheses H₀: = 74 and H_a: < 74 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) ___________ standard deviations (b) If x = 72.3, what is the conclusion using = 0.004? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z = __________

P- value = _________

c) For the test procedure with = 0.004, what is (70)? (Round your answer to four decimal places.) (70) = __________ (d) If the test procedure with = 0.004 is used, what n is necessary to ensure that (70) = 0.01? (Round your answer up to the next whole number.) n = ___________ specimens (e) 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.)