Question

Consider the following hypotheses:

H0: μ = 420

HA: μ ≠ 420

The population is normally distributed with a population standard deviation of 72. Use Table 1.

a.	Use a 1% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)

±

b-1.	Calculate the value of the test statistic with x−x− = 430 and n = 90. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

b-2.	What is the conclusion at α = 0.01?
	Do not reject H0 since the value of the test statistic is smaller than the critical value. Do not reject H0 since the value of the test statistic is greater than the critical value. Reject H0 since the value of the test statistic is smaller than the critical value. Reject H0 since the value of the test statistic is greater than the critical value.

c.	Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)

±

d-1.	Calculate the value of the test statistic with x−x− = 392 and n = 90. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

d-2.	What is the conclusion at α = 0.10?
	Do not reject H0 since the value of the test statistic is less than the negative critical value. Do not reject H0 since the value of the test statistic is not less than the negative critical value. Reject H0 since the value of the test statistic is less than the negative critical value. Reject H0 since the value of the test statistic is not less than the negative critical value.

Answer 1

a)

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are +/- 2.58
Hence reject H0 if z < -2.58 or z > 2.58

b)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (430 - 420)/(72/sqrt(90))
z = 1.32

b2)

Do not reject H0 since the value of the test statistic is smaller than the critical value.

c)

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are +/-1.64
Hence reject H0 if z < -1.64 or z > 1.64

d1)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (392 - 420)/(72/sqrt(90))
z = -3.69

d2)

Reject H0 since the value of the test statistic is less than the negative critical value