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 = 34.4	x−2x−2 = 26.4
σ12 = 89.5	σ22 = 95.8
n1 = 21	n2 = 23

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

(a)

When the population variances are known : Normal distribution is being used to calculate the confidence interval for the difference between the population means

Formula for Confidence interval for the difference between the population means

for 90% confidence level = (100-90)/100 = 0.1

/2 = 0.1/2=0.05

Z_/2 = Z_0.05 = 1.6449

90% Confidence interval for the difference between the population means

The 90% confidence interval for the difference between the population means = (3.22,12.77)

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

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

As 0 >3.22: Lower limit of the 90% confidence interval : (3.22,12.77)

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

d. Interpret the results at αα = 0.10.

• We conclude that the population means differ.