Question

Consider the following hypotheses:

H₀: μ = 410
H_A: μ ≠ 410

The population is normally distributed with a population standard deviation of 46. (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− = 421 and n = 85. (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 410.

• We conclude that the population mean differs from 410.

• We cannot conclude that the sample mean differs from 410.

• We conclude that the sample mean differs from 410.

b-1. Calculate the value of the test statistic with x−x− = 397 and n = 85. (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 410.

• We cannot conclude that the population mean differs from 410.

• We conclude that the sample mean differs from 410.

• We cannot conclude that the sample mean differs from 410.

Answer 1

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (421 - 410)/(46/sqrt(85))
z = 2.2

P-value Approach
P-value = 0.0278
As P-value < 0.1, reject the null hypothesis.

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

We conclude that the sample mean differs from 410.

#2.
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (397 - 410)/(46/sqrt(85))
z = -2.61

P-value Approach
P-value = 0.0091

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

We conclude that the population mean differs from 410.