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 = 9. The hypotheses H₀: = 73 and H_a: < 73 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 = 0.01? (Round your answers to two decimal places.)

What can you conclude?

Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73.Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73.    Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73.Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73.

(c) What is for the test procedure that rejects H₀ when

z 2.5?

(Round your answer to four decimal places.)
=  

(d) For the test procedure of part (c), what is (70)? (Round your answer to four decimal places.)
(70) =  

(e) If the test procedure of part (c) is used, what n is necessary to ensure that (70) = 0.01? (Round your answer up to the next whole number.)
n =  specimens

(f) 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

Answer to question# 1)

part a)

M = 73

M < 73

[left tailed test]

.

s = 9

n = 25

.

x = 72.3

z = (x - M) / (s/sqrt(n))

z = (72.3-73)/(9/sqrt(25))

z = -0.39

..

Answer to part b)

Z statistic = -0.39

Z critical for alpha 0.01 is : -2.33

.

Conclusion: Since Z statistic -0.39 > Z critical -2.33 , we fail to reject the null hypothesis

Thus the claim that M is less than 73 is not true

.

Answer to part c)

The alpha value that rejects Ho when z < -2.5 , is 0.00621 ...[refer to the z table]

.