Question

Consider the following hypotheses:

H₀: μ ≤ 12.6
H_A: μ > 12.6

A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Find the p-value.
  

• 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

a-2. What is the conclusion if α = 0.10?
  

• 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 = 0.10.

• We conclude that the sample mean is greater than 12.6.

• We cannot conclude that the sample mean is greater than 12.6.

• We conclude that the population mean is greater than 12.6.

• We cannot conclude that the population mean is greater than 12.6.

b-1. Calculate the p-value if the above sample mean was based on a sample of 100 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 = 0.10?
  

• 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.

b-3. Interpret the results at α = 0.10.

• We conclude that the sample mean is greater than 12.6.

• We cannot conclude that the sample mean is greater than 12.6.

• We conclude that the population mean is greater than 12.6.

• We cannot conclude that the population mean is greater than 12.6.

Answer 1