Question

Midwives claim that a water birth reduces the amount of pain the mother perceives. To    test this theory, one midwife asks six of her clients who had a water birth and eight of her clients who did not have a water birth to rate their pain on a scale of 1 to 10. The mean pain score of mothers who had a water birth was a 7.0 with a standard deviation of 1.2. The mean pain score of mothers who did not have a water birth was 9.0 with a standard deviation of 0.9. Construct and interpret an 80% confidence interval for the true difference between the pain scores of mothers who had a water birth and mothers who did not. Assume that the variances of the two populations are not equal.

Answer 1

Given:

For Water birth: = 7, s₁ = 1.2, n₁ = 6,

Non Water Birth: = 9, s₂ = 0.9, n₂ = 8,

= 0.2

The degrees of freedom for unequal variances is given by:

Therefore df = 9

The tcritical (2 tail) for = 0.2, df =9, is 1.383

The Confidence Interval is given by ()± ME, where
(x̅₁- x̅₂) = 7 – 9 = -2

The Lower Limit = -2 - 0.808 = -2.808        -2.81

The Upper Limit = -2 + 0.808 = -1.192         -1.19

The 80% Confidence Interval is (-2.81 , -1.19)