Question

In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 13.9 and 1.6, respectively. (You may find it useful to reference the appropriate table: z table or t table).

H₀: μ ≤ 13.0 against H_A: μ > 13.0

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.

• 0.01 p-value < 0.025
• p-value 0.10

• p-value < 0.01

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

a-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.

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

• We conclude that the population mean is greater than 13.

• We cannot conclude that the population mean is greater than 13.

• We conclude that the population mean differs from 13.

• We cannot conclude that the population mean differs from 13..

H₀: μ = 13.0 against H_A: μ ≠ 13.0

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.

• 0.01 p-value < 0.025

• p-value < 0.01

• p-value 0.10
• 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 13.

• We cannot conclude that the population mean is greater than 13.

• We conclude that the population mean differs from 13.

• We cannot conclude that the population mean differs from 13.

Answer 1

a1)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (13.9 - 13)/(1.6/sqrt(24))
t = 2.756

a2)

P-value Approach
P-value = 0.0056

p-value < 0.01
As P-value < 0.01, reject the null hypothesis.

a3)

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

a4)

We conclude that the population mean is greater than 13.

b1)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (13.9 - 13)/(1.6/sqrt(24))
t = 2.756

b2)

P-value = 0.0112

0.01< p-value < 0.025
As P-value >= 0.01, fail to reject null hypothesis.

b3)

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

b4)

We cannot conclude that the population mean differs from 13.