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

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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}}.
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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