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.

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

• p-value < 0.01

• 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.

• p-value < 0.01

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

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

The statistical software output for this problem is:

One sample T summary hypothesis test:

μ : Mean of population
H₀ : μ = 13
H_A : μ > 13

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
μ	13.9	0.32659863	23	2.755676	0.0056

Hence,

a - 1) Test statistic = 2.756

a - 2) p-value < 0.01

a - 3) Reject H₀ since the p-value is less than significance level.

a - 4) We conclude that the population mean is greater than 13.

b - 1) Test statistic = 2.756

b - 2) p-value < 0.01

b - 3) Reject H₀ since the p-value is less than significance level.

b - 4) We conclude that the population mean differs from 13.