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 = 27.7	x−2x−2 = 30.1
σ12 = 92.8	σ22 = 87.5
n1 = 24	n2 = 33

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.
  

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

• B.) H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• C.)H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

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

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

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

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

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

d. Interpret the results at αα = 0.01.

• A.)We conclude that the population means differ.

• B.)We cannot conclude that the population means differ.

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

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

Answer 1