Question

Constructing and Interpreting Confidence Intervals. In Exercises 13–16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Construct a 95% confidence interval for the proportion of medical malpractice lawsuits that are dropped or dismissed.

Answer 1

Solution :

n = 1228

x = 856

a ) = x / n = 856 / 1228= 0.697

1 - = 1 - 0.697 = 0.303

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

b ) Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.960 * (((0.697 * 0.303) / 1228)

= 0.026

c ) A 95% confidence interval for population proportion p is ,

- E < P < + E

0.697 - 0.026 < p < 0.697 + 0.026

0.671 < p < 0.723

d ) The proportion of medical malpractice  lawsuits that are 0.671 < p < 0.723 .