Consider a paint-drying situation in which drying time for atest specimen is normally distributed with ? = 9. Thehypotheses H0: ? = 75 andHa: ? < 75 are to be tested using arandom sample of n = 25 observations.
(a) How many standard deviations (of X) below the nullvalue is x = 72.3? (Round your answer to two decimalplaces.)
standard deviations
(b) If x = 72.3, what is the conclusion using ? =0.002?
Calculate the test statistic and determine the P-value.(Round your test statistic to two decimal places and yourP-value to four decimal places.)
State the conclusion in the problem context.
Reject the null hypothesis. There is not sufficient evidence toconclude that the mean drying time is less than 75.Do not rejectthe null hypothesis. There is not sufficient evidence to concludethat the mean drying time is less than75. Do not reject the null hypothesis. Thereis sufficient evidence to conclude that the mean drying time isless than 75.Reject the null hypothesis. There is sufficientevidence to conclude that the mean drying time is less than 75.
(c) For the test procedure with ? = 0.002, what is?(70)? (Round your answer to four decimal places.)
?(70) =
(d) If the test procedure with ? = 0.002 is used, whatn 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 theprobability of a type I error when ? = 76? (Round youranswer to four decimal places.)
