A 95 condence interval using the conservative value for the

A 95% condence interval (using the conservative value for the degrees of freedom) for µ1 µ2, based on two independent samples of sizes 18 and 20, respectively, gives us (45.6, 56.7).

(a) What was the observed dierence between the two sample means ¯ x1 and ¯ x2?

(b) What would be the margin of error for a 99% condence interval for µ1 µ2?

(c) Answer each of the following questions with yes, no, or can’t tell.

i. Is the dierence between the two population means, µ1 µ2, included in the 95% condence interval?

ii. Is the dierence between the two sample means, ¯ x1 ¯ x2, included in the 95% condence interval?

iii. Is the probability that the dierence between the two population means, µ1 µ2, falls between 45.6 and 56.7 equal to 0.95?

iv. If larger samples were used to calculate the condence interval, would it include more values for the dierence between the two population means?

Solution