Question

In order to conduct a hypothesis test for the population mean, a random sample of 28 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 17.9 and 1.5, respectively. (You may find it useful to reference the appropriate table: z table or t table).

H₀: μ ≤ 17.5 against H_A: μ > 17.5

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

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

  

a-3. At the 1% 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.

a-4. Interpret the results at αα = 0.01.

• We cannot conclude that the population mean is greater than 17.5.

• We conclude that the population mean is greater than 17.5.

• We cannot conclude that the population mean differs from 17.5.

• We conclude that the population mean differs from 17.5..

H₀: μ = 17.5 against H_A: μ ≠ 17.5

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 0.10
• 0.01 p-value < 0.025

• p-value < 0.01

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

b-3. At the 1% 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 = 0.01.

• We conclude that the population mean is greater than 17.5.

• We cannot conclude that the population mean is greater than 17.5.

• We conclude that the population mean differs from 17.5.

• We cannot conclude that the population mean differs from 17.5.

Answer 1