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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

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;HA:12 0
  • H0:12 0;HA:12< 0
  • H0:12 0;HA: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.

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