A random sample of 322 medical doctors showed that 180 had a solo practice. a) L
ID: 3216576 • Letter: A
Question
A random sample of 322 medical doctors showed that 180 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 95% confidence interval for p. (Use 3 decimal places.)
lower limit
upper limit
Give a brief explaination of the meaning of the interval.
- 95% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.
- 95% of the all confidence intervals would include the true proportion of physicians with solo practices.
- 5% of the all confidence intervals would include the true proportion of physicians with solo practices.
- 5% 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 p(hat).
- Report p( hat) aling with the margin of error.
- Report the margin of error.
What is the margin of error based on a 95% confidence interval. (Use 3 decimal places.)
Explanation / Answer
Answer to part a)
The point estimate is = x/n
x = 180
n = 322
Point estimate P^ = 180/322 = 0.5590
.
Answer to part b)
Formula of 95% confidence interval is :
P^ - Z * SE , P^ + Z * SE
Se = square root of [P^*(1-P^)/n]
Se = square root [0.5590*0.4410/322]
SE = 0.0277
.
For 95% confidence level Z = 1.96
.
On plugging all the values we get:
0.5590 - 1.96 * 0.0277 , 0.5590 + 1.96 * 0.0277
0.5590 - 0.05429 , 0.5590 + 0.05429
0.5047 , 0.6133
.
The first interpretation is correct
.
Answer to part c)
The best way to report is by quoting the confidence interval in the report, It provides as a range that may contain the true proportion
.
Answer to part d)
The margin of error = Z*SE
Margin of error = 1.96 * 0.0277 = 0.05429
Margin of error = 0.054 .[Three decimal places]
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