Question

A random sample of 332 medical doctors showed that 170 had a solo

practice.

(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.)

(b) Find a 98% confidence interval for p. (Use 3 decimal places.)

lower limit   

upper limit   

Give a brief explanation of the meaning of the interval.

2% of the all confidence intervals would include the true proportion of physicians with solo practices.

98% of the all confidence intervals would include the true proportion of physicians with solo practices.    

2% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.

98% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.

(c) As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice?

Report the confidence interval.

Report p̂.    

Report p̂ along with the margin of error.

Report the margin of error.

What is the margin of error based on a 98% confidence interval? (Use 3 decimal places.)

22.

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 26 out of 830 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 mortality rate) when caught and released using barbless hooks. 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 the interval.

1% of the confidence intervals created using this method would include the true catch-and-release mortality rate.

99% of the confidence intervals created using this method would include the true catch-and-release mortality rate.    

1% of all confidence intervals would include the true catch-and-release mortality rate.

99% of all confidence intervals would include the true catch-and-release mortality rate.

(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.

 

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