Question

1. Consider the following hypotheses:

H₀: μ = 420
H_A: μ ≠ 420

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

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

a-2. What is the conclusion at the 1% significance level?
  

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

• 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.

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

a-3. Interpret the results at αα = 0.01.

• We conclude that the population mean differs from 420.

• We cannot conclude that the population mean differs from 420.

• We conclude that the sample mean differs from 420.

• We cannot conclude that the sample mean differs from 420.

b-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 intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

b-2. What is the conclusion at the 10% 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 = 0.10.

• We conclude that the population mean differs from 420.

• We cannot conclude that the population mean differs from 420.

• We conclude that the sample mean differs from 420.

• We cannot conclude that the sample mean differs from 420.

Answer 1