Question

4. 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−1 = −1.6	x−2 = −16.3
s12 = 8.9	s22 = 7.9
n1 = 23	n2 = 15

a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Confidence interval is to .

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 includes the hypothesized value of 0.

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

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

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

d. Interpret the results at αα = 0.05.

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

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

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

Answer 1

a.

Formula for Confidence Interval for Difference in two Population means when population Standard deviation are not known but equal

for 95% confidence level = (100-95)/100 =0.05

/2 = 0.05/2 =0.025

Degrees of freedom: df =n₁+n₂-2 = 23+15-2 =36

95% confidence interval for the difference between the population means.

Confidence interval is 12.7363 to 16.6637

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

H₀: ; H_A:

c.

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

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

d. Interpret the results at αα = 0.05.

• We conclude that the population means differ.