Question

8. A statistical study found that when nurses made home visits to pregnant teenagers to provide support services, discourage smoking and otherwise provide care, the sample mean birth weight of the babies was higher for this treatment group (3285 grams) than for the control group (2922 grams) when the visits began before mid-gestation. There were 21 patients in the treatment group and 11 in the control group. Suppose the birth weights for both groups follow a normal distribution. Assume that the population standard deviation in each sample is 500 grams.

1. 1. Construct and interpret a 95% Z confidence interval for μ₁ – μ₂.
2. 2. Test at level of significance α = 0.05 whether the population birth weight differs between the two groups. Use the Z test.

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = 1.9506   1.95

Test Criteria :-
Reject null hypothesis if


Result :- Fail to Reject Null Hypothesis

Confidence interval :-


Lower Limit =
Lower Limit = -1.7431
Upper Limit =
Upper Limit = 727.7431
95% Confidence interval is ( -1.7431 , 727.7431 )