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 = 28.5	x−2x−2 = 29.8
σ12 = 96.9	σ22 = 87.0
n1 = 29	n2 = 25

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

Part a)

Confidence interval :-

Critical value Z(α/2) = Z (0.01 /2) = 2.576 ( From Z table )

Lower Limit =
Lower Limit = -8.03
Upper Limit =
Upper Limit = 5.43
99% Confidence interval is ( -8.03 , 5.43 )

Part b)

H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

Part c)

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

Part d)

We cannot conclude that the population means differ.