Question

Consider the following sample data drawn independently from normally distributed populations with unknown but equal population variances. (You may find it useful to reference the appropriate table: z table or t table)

Sample 1			Sample 2
	12.1			8.9
	9.5			10.9
	7.3			11.2
	10.2			10.6
	8.9			9.8
	9.8			9.8
	7.2			11.2
	10.2			12.1

Click here for the Excel Data File


a. Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. 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

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

b-3. Do you reject the null hypothesis at the 1% level?

• Yes, since the value of the p-value is greater than the significance level.

• No, since the value of the p-value is greater than the significance level.

• Yes, since the value of the p-value is less than the significance level.

• No, since the value of the p-value is less than the significance level.

c. Do you reject the null hypothesis at the 10% level?

• Yes, since the value of the p-value is greater than the significance level.

• No, since the value of the p-value is greater than the significance level.

• Yes, since the value of the p-value is less than the significance level.

• No, since the value of the p-value is less than the significance level.

Answer 1

The statistical software output for this problem is :

H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

Test statistics = -1.724

0.05 ≤ p-value < 0.10

(b-3)

No, since the value of the p-value is greater than the significance level.

(c)

Yes, since the value of the p-value is less than the significance level.

answered by: anonymous