According to Reader's Digest, 30% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 400 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p) = 0.3 (to 2 decimals) 0.0235 (to 4 decimals) b. What is the probability that the sample proportion will be within +0.03 of the population proportion? Round your answer to four decimals. c. What is the probability that the sample proportion will be within +0.05 of the population proportion? Round your answer to four decimals. d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would decrease This is because the increase in the sample size makes the standard error, o5, larger
According to Reader's Digest, 30% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 400 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p) = 0.3 (to 2 decimals) 0.0235 (to 4 decimals) b. What is the probability that the sample proportion will be within +0.03 of the population proportion? Round your answer to four decimals. c. What is the probability that the sample proportion will be within +0.05 of the population proportion? Round your answer to four decimals. d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would decrease This is because the increase in the sample size makes the standard error, o5, larger
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![According to Reader's Digest, 30% of primary care doctors think their patients receive unnecessary medical care. Use the z-table.
a. Suppose a sample of 400 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care.
\[
E(\bar{p}) = \boxed{0.3} \text{ (to 2 decimals)}
\]
\[
\sigma_{\bar{p}} = \boxed{0.0235} \text{ (to 4 decimals)}
\]
b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals.
(Probability answer box)
c. What is the probability that the sample proportion will be within ±0.05 of the population proportion? Round your answer to four decimals.
(Probability answer box)
d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
The probabilities would (dropdown box) \boxed{\text{decrease}}. This is because the increase in the sample size makes the standard error, \(\sigma_{\bar{p}}\), (dropdown box) \boxed{\text{larger}}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba6262a5-d997-4fde-9cea-b71e30254a96%2Ff1eb52d4-14f0-4939-9637-11618751ca44%2F6dhzeg9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to Reader's Digest, 30% of primary care doctors think their patients receive unnecessary medical care. Use the z-table.
a. Suppose a sample of 400 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care.
\[
E(\bar{p}) = \boxed{0.3} \text{ (to 2 decimals)}
\]
\[
\sigma_{\bar{p}} = \boxed{0.0235} \text{ (to 4 decimals)}
\]
b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals.
(Probability answer box)
c. What is the probability that the sample proportion will be within ±0.05 of the population proportion? Round your answer to four decimals.
(Probability answer box)
d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
The probabilities would (dropdown box) \boxed{\text{decrease}}. This is because the increase in the sample size makes the standard error, \(\sigma_{\bar{p}}\), (dropdown box) \boxed{\text{larger}}.
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