Consider the following data drawn independently from normally distributed populations:(You may find it useful to reference the appropriate table:z tableort table)

X1= 12.0 X2 = 24.5

s₁²= 8.5 s₂²= 8.5

n₁= 28 n₂= 28

a.Construct the 90% 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.)

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

• H₀:₁₂= 0;H_A:₁₂ 0
• H₀:₁₂ 0;H_A:₁₂< 0
• H₀:₁₂ 0;H_A:₁₂> 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

= 0.1.

• 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.