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 = 30.9	x−2x−2 = 25.9
σ12 = 93.5	σ22 = 96.0
n1 = 30	n2 = 25

a. Construct the 90% 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?
  

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

• Yes, since the confidence interval does not include 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 = 0.10.

• We cannot conclude that the population means differ.

• We conclude that the population means differ.

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

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

Answer 1

c)

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

d)

• We conclude that the population means differ.