According to Reader's Digest, 43% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 290 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients rece (to 2 decimals) (to 4 decimals) E(F) %3D 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.
According to Reader's Digest, 43% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 290 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients rece (to 2 decimals) (to 4 decimals) E(F) %3D 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.
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*, 43% of primary care doctors think their patients receive unnecessary medical care. Use the z-table.
a. Suppose a sample of 290 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary care.
\[
E(\hat{p}) = \_\_\_\_ \text{ (to 2 decimals)}
\]
\[
\sigma_{\hat{p}} = \_\_\_\_ \text{ (to 4 decimals)}
\]
b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals.
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 \_\_\_\_\_\_ \text{Select your answer} \_\_\_\_\_. This is because the increase in the sample size makes the standard error, \(\sigma_{\hat{p}}\), \_\_\_\_\_\_ \text{Select your answer} \_\_\_\_\_.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10a3752c-32c6-4433-905d-da29834997c3%2F7e3f437b-3dca-4f69-bc99-f84a96ee541e%2F3h4kxu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to *Reader's Digest*, 43% of primary care doctors think their patients receive unnecessary medical care. Use the z-table.
a. Suppose a sample of 290 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary care.
\[
E(\hat{p}) = \_\_\_\_ \text{ (to 2 decimals)}
\]
\[
\sigma_{\hat{p}} = \_\_\_\_ \text{ (to 4 decimals)}
\]
b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals.
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 \_\_\_\_\_\_ \text{Select your answer} \_\_\_\_\_. This is because the increase in the sample size makes the standard error, \(\sigma_{\hat{p}}\), \_\_\_\_\_\_ \text{Select your answer} \_\_\_\_\_.
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