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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 = ?10.5	x?2x?2 = ?16.8
s12 = 7.9	s22 = 9.3
n1 = 15	n2 = 20

a. Construct the 95% confidence interval for thedifference between the population means. Assume the populationvariances are unknown but equal. (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 population mean 1 is greater than populationmean 2.

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

• We conclude that the population means differ.

• We cannot conclude that the population means differ.