Question

Consider the following hypotheses:

H₀: μ ≤ 30.4
H_A: μ > 30.4

A sample of 55 observations yields a sample mean of 31.9. Assume that the sample is drawn from a normal population with a population standard deviation of 5.2. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Find the p-value.
  

• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

• p-value < 0.01

• 0.01 p-value < 0.025

a-2. What is the conclusion if α = 0.01?
  

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

• Reject H₀ since the p-value is smaller than α.

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

• Do not reject H₀ since the p-value is smaller than α.

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

• We conclude that the sample mean is greater than 30.4.

• We cannot conclude that the sample mean is greater than 30.4.

• We conclude that the population mean is greater than 30.4.

• We cannot conclude that the population mean is greater than 30.4.

b-1. Calculate the p-value if the above sample mean was based on a sample of 120 observations.
  

• p-value < 0.01

• 0.01 p-value < 0.025
• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

b-2. What is the conclusion if α = 0.01?
  

• Reject H₀ since the p-value is smaller than α.

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

• Do not reject H₀ since the p-value is smaller than α.

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

b-3. Interpret the results at α = 0.01.

• We conclude that the sample mean is greater than 30.4.

• We cannot conclude that the sample mean is greater than 30.4.

• We conclude that the population mean is greater than 30.4.

• We cannot conclude that the population mean is greater than 30.4.

Answer 1

a-1)

0.01 p-value < 0.025

a-2)

Do not reject H₀ since the p-value is greater than α.

a-3)

We cannot conclude that the population mean is greater than 30.4.

b-1)p-value < 0.01

b-2)Reject H₀ since the p-value is smaller than α.

b-3)

We conclude that the population mean is greater than 30.4.