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 10,341 convicts who escaped from
certain prisons, only 7535 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 |

Give a brief statement of the meaning of the confidence
interval.

99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.99% of all confidence intervals would include the true proportion of recaptured escaped convicts. 1% of all confidence intervals would include the true proportion of recaptured escaped convicts.1% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

(c) Is use of the normal approximation to the binomial justified in
this problem? Explain.

No; *np* < 5 and *nq* > 5.No; *np*
> 5 and *nq* < 5. Yes;
*np* < 5 and *nq* < 5.Yes; *np* > 5
and *nq* > 5.

Answer #1

a)

point estimate for *p* =0.7287

b)

lower limit =0.717

upper limit =0.740

99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

c)

.Yes; *np* > 5 and *nq* > 5

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