Question

The birth weights for two groups of babies were compared in a study. In one group the mothers took a zinc supplement during pregnancy. In another group, the mothers took a placebo. A sample of 138 babies in the zinc group had a mean birth weight of 3016 grams. A sample of 111 babies in the placebo group had a mean birth weight of 3343 grams. Assume that the population standard deviation for the zinc group is 790 grams, while the population standard deviation for the placebo group is 516 grams. Determine the 95% confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.

Step 1 of 3: Find the point estimate for the true difference between the population means.

Step 2 of 3: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

Step 3 of 3: Construct the 95% confidence interval. Round your answers to the nearest whole number.

Answer 1

n1= 138, = 3016,  = 790,

n2= 111, = 3343,   = 516,

c = 95%

Step 1

point estimate = 3016 - 3343

point estimate for the true difference between the population means is = -327

Step 2

formula for margin of error is

Where Zc is the z critical value for c= 95%

Zc= 1.96

= 163.059355

margin of error = 163.059355

Step 3

formula for confidence interval is

-327 163.059355

-490.059355 <   < -163.940645

-490 <   < -164

Thus we get confidence interval as ( -490 , -164)