Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. Case studies showed that out of 10,596 convicts who escaped from certain prisons, only 7911 were recaptured.

(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

lower limit

upper limit

Answer 1

Case studies showd that out of 10,596 convicts who escaped from certain prisons, only 7911 were recaptured.

Question (a)

p represents the proportion of all escaped convicts who would eventually be recaptured.

We have to find the point estimate of p.

Now, we know that the ample proportion is an unbiased estimator of the population proportion.

Here, the sample proportion is

So, a point estimate for p, rounded off to four decimal places is 0.7466.

Question (b)

We have to find a 99% confidence interval for p.

Now, for 99% confidence interval, the z-value is given by z=2.576

The sample size is n=10596.

The sample proportion is p=0.7466.

Now, we know that the 99% confidence interval is given by

The answer rounded to three decimal places is

Lower limit=0.736

Upper limit=0.758