Question

A 90% confidence interval for the difference between the means of two independent populations with unknown population standard deviations is found to be (-0.2, 5.4).

Which of the following statements is/are correct? CHECK ALL THAT APPLY.

A. A two-sided two-sample t-test testing for a difference between the two population means is not rejected at the 10% significance level.
B. The standard error of the difference between the two observed sample means is 2.6.
C. A two-sided paired t-test testing for a difference between the two population means is not rejected at the 10% significance level.
D. A two-sided two-sample t-test testing for a difference between the two population means is rejected at the 10% significance level.
E. A two-sided paired t-test testing for a difference between the two population means is rejected at the 10% significance level.
F. None of the above.

Answer 1

A. A two-sided two-sample t-test testing for a difference between the two population means is not rejected at the 10% significance level

Margin of error = (upper bound - lower bound)/2
= [5.4 - (-0.2)] / 2
= 2.8
Margin of error = Confidence coefficient*Standard error (SE)
Therefore,
2.8 = 1.645*SE
SE = 2.8/1.645 = 1.7021