Question

For these problems, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 608 potsherds was found, of which 354 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)

.5822

(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

lower limit:

upper limit:

A random sample of 5913 physicians in Colorado showed that 3008 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)

.5087

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

lower limit:

upper limit:

Case studies showed that out of 10,307 convicts who escaped from certain prisons, only 7770 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.)

.7539

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

lower limit:

upper limit:

Answer 1

(1)

(a)

n = 608

= 354/608

= 0.5822

So,

point estimate for p. = = 0.5822

(b)

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

So,

Answer is:

(0.543, 0.621)

(2)

(a)

n = 5913

= 3008/5913

= 0.5087

So,

point estimate for p. = = 0.5087

(b)

= 0.01

From Table, critical values of Z = 2.576

Confidence Interval:

So,

Answer is:

(0.492, 0.525)

(3)

(a)

n = 10307

= 7770/10307 = 0.7539

So,

point estimate for p. = = 0.7539

(b)

= 0.01

From Table, critical values of Z = 2.576

Confidence Interval:

So,

Answer is:

(0.743, 0.765)