Question

Carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A. In a random sample of 512 judges, it was found that 287 were introverts.

Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)

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

lower limit
upper limit

B.

A random sample of 5400 physicians in Colorado showed that 3359 provided at least some charity care (i.e., treated poor people at no cost).

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.)

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

lower limit
upper limit

Answer 1

Solution :

Given that,

A.

Point estimate = sample proportion = = x / n = 287 / 512 = 0.5605

1 - = 1 - 0.5605 = 0.4395

Z_/2 = 2.576

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

= 2.576 * (((0.5605 * 0.4395) / 512)

= 0.057

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5605 - 0.057 < p < 0.5605 + 0.057

0.50 < p < 0.62

The 99% confidence interval for the population proportion p is : 0.50 , 0.62

Lower limit = 0.50

Upper limit = 0.62

B.

Point estimate = sample proportion = = x / n = 3359 / 5400 = 0.6220

1 - = 1 - 0.6220 = 0.378

Z_/2 = 2.576

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

= 2.576 * (((0.6220 * 0.378) / 5400)

= 0.017

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.6220 - 0.017 < p < 0.6220 + 0.017

0.605 < p < 0.639

The 99% confidence interval for the population proportion p is : 0.605 , 0.639

Lower limit = 0.605

Upper limit = 0.639