Question

In order to conduct a hypothesis test for the population mean, a random sample of 12 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 16.6 and 2.2, respectively.

H₀: μ ≤ 14.9 against H_A: μ > 14.9

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.

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

a-3. At the 5% 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 = 0.05.

• We conclude that the population mean is greater than 14.9.

• We cannot conclude that the population mean is greater than 14.9.

• We conclude that the population mean differs from 14.9.

• We cannot conclude that the population mean differs from 14.9.

H₀: μ = 14.9 against H_A: μ ≠ 14.9

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.

• 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

b-3. At the 5% significance level, what is the conclusion?

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

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

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

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

b-4. Interpret the results at αα = 0.05.

• We cannot conclude that the population mean is greater than 14.9.

• We conclude that the population mean is greater than 14.9.

• We cannot conclude that the population mean differs from 14.9.

• We conclude that the population mean differs from 14.9.

Answer 1