Question

Consider the following hypotheses:

H₀: μ = 360
H_A: μ ≠ 360

The population is normally distributed with a population standard deviation of 73. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Calculate the value of the test statistic with x−x− = 389 and n = 80. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

a-2. What is the conclusion at the 10% significance level?
  

• Do not reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is less than the significance level.

• Reject H₀ since the p-value is greater than the significance level.

• Reject H₀ since the p-value is less than the significance level.

a-3. Interpret the results at αα = 0.10.

• We cannot conclude that the population mean differs from 360.

• We conclude that the population mean differs from 360.

• We cannot conclude that the sample mean differs from 360.

• We conclude that the sample mean differs from 360.

b-1. Calculate the value of the test statistic with x−x− = 335 and n = 80. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

b-2. What is the conclusion at the 5% significance level?
  

• Reject H₀ since the p-value is greater than the significance level.

• Reject H₀ since the p-value is less than the significance level.

• Do not reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is less than the significance level.

b-3. Interpret the results at αα = 0.05.

• We conclude that the population mean differs from 360.

• We cannot conclude that the population mean differs from 360.

• We conclude that the sample mean differs from 360.

• We cannot conclude that the sample mean differs from 360.

Answer 1

Part a)

Test Statistic :-


Z = 3.5532   3.55

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

P value = 2 * P ( Z > 3.55 ) = 0.00038

Decision based on P value
P value = 2 * P ( Z > 3.55 ) = 0.00038
Reject null hypothesis if P value <    level of significance
P - value = 0.00038 < 0.10 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

• Reject H₀ since the p-value is less than the significance level.

• We conclude that the population mean differs from 360.

Part b)

Test Statistic :-


Z = -3.0631 -3.06

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

P value = 2 * P ( Z > 3.55 ) = 0.00038

Decision based on P value
P value = 2 * P ( Z > 3.55 ) = 0.00219
Reject null hypothesis if P value <    level of significance
P - value = 0.00219 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject H₀ since the p-value is less than the significance level.

We conclude that the population mean differs from 360.