Question

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

In a random sample of 502 judges, it was found that 287 were introverts.

(a) Let p represent the proportion of all judges who are introverts. 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 two decimal places.)

lower limit
upper limit

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

A random sample of 5886 physicians in Colorado showed that 3359 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.)


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

lower limit
upper limit

Answer 1

Solution :  

Given that,

n = 502

x = 287

(a)

Point estimate = sample proportion = = x / n = 287 / 502 = 0.5717

1 - = 1 - 0.5717 = 0.4283

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.5717 * 0.4283) / 502)

= 0.06

(b)

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5717 - 0.06 < p < 0.5717 + 0.06

0.51< p < 0.63

The 99% confidence interval for the population proportion p is : 0.51 , 0.63

lower limit = 0.51

Upper limit = 0.63

x = 3359

n = 5886

(a)

Point estimate = sample proportion = = x / n = 3359 / 5886 = 0.5707

1 - = 1 - 0.5707 = 0.4293

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.5707 * 0.4293) / 5886)

= 0.017

(b)

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5707 - 0.017 < p < 0.5707 + 0.017

0.554 < p < 0.588

The 99% confidence interval for the population proportion p is : 0.554 , 0.588

Lower limit = 0.554

Upper limit = 0.588