Question

The 98% confidence interval about the proportion of applicants who were accepted to a medical school in 2011 is (0.455, 0.464).

1. a) (2 points) Identify the point estimate for the proportion of applicants who were accepted to a medical school.

2. b) (2 points) Identify the margin of error for the proportion of applicants who were accepted to a medical school.

Answer 1

Confidence interval in terms of sample proportion and margin of error E is represented as

( - E , + E)

Comparing these two confidence intervals we get,

- E = 0.455 and + E = 0.464

Adding two equations

2 = 0.455 + 0.464

= 0.4595

Point estimate of p = = 0.4595 ( = 0.460 Rounded to three decimals)

b)

Put value of is equation + E = 0.464 and solve for E

0.4595 + E = 0.464

E = 0.0045 ( = 0.005 rounded to three decimals)