Question

Investigators are trying to determine if the contamination of a town well led to significant increases in adverse health effects. During the period of time when water was consumed from this contaminated well, there were 16 birth defects among 414 births. After this well was shut off, there were 3 birth defects among 228 births. Investigators asked to determine if the rate of birth defects was higher when the contaminated well was in use.

(a) Estimate the probability of a birth defect when the contaminated water was consumed. Estimate the probability of a birth defect when the contaminated well was shut off.

(b) Calculate the 95% confidence interval for the true population proportion of birth defects when the contaminated water was consumed. Calculate the 95% confidence interval for the true population proportion of birth defects when the well was shut off.

(c) Test the claim that the contaminated well was not associated with an increase in the rate of birth defects in the community at the alpha = 0.05 level, by using the two-proportion z test.

(d) Calculate a 95% confidence interval for the true difference between the proportions of birth defects when the contaminated well was in use versus when the well was shut down.

Answer 1

(a)

The probability of a birth defect when the contaminated water was consumed is

The probability of a birth defect when the contaminated well was shut off is

(b)

The  95% confidence interval for the true population proportion of birth defects when the contaminated water was consumed:

The 95% confidence interval for the true population proportion of birth defects when the well was shut off is:

(c)

Conclusion: We cannot conclude that the contaminated well was not associated with an increase in the rate of birth defects in the community at the alpha = 0.05 level.

(d)