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 answer to 2 decimal places.)

   

Test statistic

   

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

   

Test statistic

   

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

Answer 1

Given the following hypotheses

H0: μ = 420

HA: μ ≠ 420

and the population is normally distributed with a population standard deviation of = 72.

Based on the hypothesis it will be a two-tailed test and since the population standard deviation is known hence Z distribution is applicable for hypothesis testing.

a) Critical value:

The critical values for rejection region is computed uisng the excel formula for normal distribuution which is computed as =NORM.S.INV(0.005), thus the Zc is computed as -2.58 and 2.58

So, reject Ho if Z <-Zc or Z> Zc.

b1) Test statistic:

Given the sample size is n = 90 and the sample mean as = 430

The test statistic is calculated as:

Z = 1.32

b2. Conclusion:

Do not reject the Ho since the value of test statistic is less than the critical value.

c) Critical values at 0.10 level of significance:

The critical values for rejection region is computed uisng the excel formula for normal distribuution which is computed as =NORM.S.INV(0.05), thus the Zc is computed as -1.64 and 1.64.

d) Conclusion at 0.10 level of significance.

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