Question

here was concern among health officials in the Windham area that an unusually large percentage of newborn babies had abnormally low birth weights (less than 5.5 lbs.). A sample of 250 newborns showed 20 of these babies had abnormally low birth weight.

Construct a 95% confidence interval for the true proportion of babies in the Windham area who have abnormally low birth weight.

Answer 1

We need to construct the 95% confidence interval for the population proportion.

Favorable Cases X =	20
Sample Size N =	250

The sample proportion is computed as follows:

The sample size N = 250 and the number of favorable cases X = 20:

The critical value for α = 0.05 is .

The corresponding confidence interval is computed as shown below:

Therefore, the 95% confidence interval for the population proportion is 0.046 < p < 0.114, which indicates that we are 95% confident that the true population proportion p is contained by the interval (0.046, 0.114)

The 95% confidence interval for the true proportion of babies in the Windham area who have abnormally low birth weight is (0.046, 0.114).