Question

Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

x−1x−1 = 24.0	x−2x−2 = 29.3
σ12 = 90.4	σ22 = 90.5
n1 = 32	n2 = 32

a. Construct the 99% confidence interval for the difference between the population means. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
  

b. Specify the competing hypotheses in order to determine whether or not the population means differ.
  

• 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

c. Using the confidence interval from part a, can you reject the null hypothesis?
  

• Yes, since the confidence interval does not include the hypothesized value of 0.

• No, since the confidence interval includes the hypothesized value of 0.

• Yes, since the confidence interval includes the hypothesized value of 0.

• No, since the confidence interval does not include the hypothesized value of 0.

d. Interpret the results at αα = 0.01.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

• We conclude that population mean 2 is greater than population mean 1.

• We cannot conclude that population mean 2 is greater than population mean 1.

Answer 1

a)

z = 2.576 for 99%

	1	2
variance	90.4	90.5
sd	9.507891	9.513149

The 99% confidence interval for μ1​−μ2​ is −11.424<μ1​−μ2​<0.824

= (-11.42,0.82)

b)

option A) H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

c)

option B) No, since the confidence interval includes the hypothesized value of 0.

d)

option B)

We cannot conclude that the population means differ