Question

In: Statistics and Probability

For this problem, carry at least four digits after the decimal in your calculations. Answers may...

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 5400 physicians in Colorado showed that 2927 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    


Give a brief explanation of the meaning of your answer in the context of this problem.

99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.    1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.


(c) Is 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.

Solutions

Expert Solution

Solution:

Given:

n = sample size = Number of physicians in Colorado selected in sample = 5400

x = Number of physicians in Colorado provided at least some charity care = 2927

Part a) p = the proportion of all Colorado physicians who provide some charity care.

Find a point estimate for p.

Part b) Find a 99% confidence interval for p.

where

Zc is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Zc = 2.575

Thus

Thus

and

Give a brief explanation of the meaning of your answer in the context of this problem.

99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.  

Since confidence interval is an interval estimate for population parameter.

Part c) Is the normal approximation to the binomial justified in this problem? Explain.

n*p = 5400 *0.5420 = 2927 > 5 and n*q = n* (1-p) = 5400 * (1-0.5420) = 2473 > 5

Thus correct answer is:

Yes; np > 5 and nq > 5.


Related Solutions

For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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 66 professional actors, it was found that 43 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% 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...
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 5967 physicians in Colorado showed that 3224 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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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 66 professional actors, it was found that 41 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% 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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try. (a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80% sure that the...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 20 out of 860 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish. (a) Let p represent the proportion of all pike and trout that die (i.e., p is the...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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 5913 physicians in Colorado showed that 3035 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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
For this problem, 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 586 potsherds was found, of which 358 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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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...
For this problem, carry at least four digits after the decimal in your calculations. Answers may...
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 5140 permanent dwellings on an entire reservation showed that 1578 were traditional hogans. (a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answer...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT