Consider the following data drawn independently from normallydistributed populations: (You may find it useful toreference the appropriate table: z tableor t table)

x?1x?1 = 25.7	x??2x¯2 = 30.6
?12 = 98.2	?22 = 87.4
n1 = 20	n2 = 25

a. Construct the 95% confidence interval for thedifference between the population means. (Negative valuesshould be indicated by a minus sign. Round all intermediatecalculations to at least 4 decimal places and final answers to 2decimal places.)

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

• H₀: ?₁ ??₂ = 0; H_A:?₁ ? ?₂ ? 0

• H₀: ?₁ ??₂ ? 0; H_A:?₁ ? ?₂ < 0

• H₀: ?₁ ??₂ ? 0; H_A:?₁ ? ?₂ > 0

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

• Yes, since the confidence interval includes the hypothesizedvalue of 0.

• No, since the confidence interval includes the hypothesizedvalue of 0.

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

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

d. Interpret the results at   ?? =0.05.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

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

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