Question

In order to conduct a hypothesis test for the population mean, a random sample of 9 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 14.0 and 1.4, respectively. (You may find it useful to reference the appropriate table: z table or t table).

H₀: μ ≤ 13.3 against H_A: μ > 13.3

a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

• p-value < 0.01

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

a-3. At the 10% significance level, what is the conclusion?

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

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

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

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

a-4. Interpret the results at αα = 0.1.

• We conclude that the population mean is greater than 13.3.

• We cannot conclude that the population mean is greater than 13.3.

• We conclude that the population mean differs from 13.3.

• We cannot conclude that the population mean differs from 13.3..

H₀: μ = 13.3 against H_A: μ ≠ 13.3

b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

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

• p-value < 0.01

• 0.01 p-value < 0.025
• p-value 0.10

b-3. At the 10% significance level, what is the conclusion?

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

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

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

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

b-4. Interpret the results at αα = 0.1.

• We conclude that the population mean is greater than 13.3.

• We cannot conclude that the population mean is greater than 13.3.

• We conclude that the population mean differs from 13.3.

• We cannot conclude that the population mean differs from 13.3.

Answer 1