(a) Suppose a sample of 320 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 0.36, 0.39, 0.42, 0.45, 0.48. The curve enters the viewing window near 0.36 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.48. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −1.58, −0.58, 0.42, 1.42, 2.42, 3.42. The curve enters the viewing window near −1.58 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 2.42. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −0.06, −0.03, 0, 0.03, 0.06. The curve enters the viewing window near −0.06 just above the horizontal axis and curves up to the right and reaches a maximum near 0. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.06. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −0.03, 0, 0.03, 0.06, 0.09. The curve enters the viewing window near −0.03 just above the horizontal axis and curves up to the right and reaches a maximum near 0.03. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.09. (b) What is the probability that the sample proportion will be within ±0.03 of the population proportion? (Round your answer to four decimal places.) (c) What is the probability that the sample proportion will be within ±0.05 of the population proportion? (Round your answer to four decimal places.) (d) What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
(a) Suppose a sample of 320 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 0.36, 0.39, 0.42, 0.45, 0.48. The curve enters the viewing window near 0.36 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.48. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −1.58, −0.58, 0.42, 1.42, 2.42, 3.42. The curve enters the viewing window near −1.58 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 2.42. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −0.06, −0.03, 0, 0.03, 0.06. The curve enters the viewing window near −0.06 just above the horizontal axis and curves up to the right and reaches a maximum near 0. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.06. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: −0.03, 0, 0.03, 0.06, 0.09. The curve enters the viewing window near −0.03 just above the horizontal axis and curves up to the right and reaches a maximum near 0.03. The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.09. (b) What is the probability that the sample proportion will be within ±0.03 of the population proportion? (Round your answer to four decimal places.) (c) What is the probability that the sample proportion will be within ±0.05 of the population proportion? (Round your answer to four decimal places.) (d) What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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You may need to use the appropriate appendix table or technology to answer this question.
According to Reader's Digest, 42 percent of primary care doctors think their patients receive unnecessary medical care.
(a)
Suppose a sample of 320 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care.
A bell-shaped curve is above a horizontal axis labeled p.
- In order of left to right, the ticks on the horizontal axis are labeled: 0.36, 0.39, 0.42, 0.45, 0.48.
- The curve enters the viewing window near 0.36 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42.
- The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.48.
A bell-shaped curve is above a horizontal axis labeled p.
- In order of left to right, the ticks on the horizontal axis are labeled: −1.58, −0.58, 0.42, 1.42, 2.42, 3.42.
- The curve enters the viewing window near −1.58 just above the horizontal axis and curves up to the right and reaches a maximum near 0.42.
- The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 2.42.
A bell-shaped curve is above a horizontal axis labeled p.
- In order of left to right, the ticks on the horizontal axis are labeled: −0.06, −0.03, 0, 0.03, 0.06.
- The curve enters the viewing window near −0.06 just above the horizontal axis and curves up to the right and reaches a maximum near 0.
- The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.06.
A bell-shaped curve is above a horizontal axis labeled p.
- In order of left to right, the ticks on the horizontal axis are labeled: −0.03, 0, 0.03, 0.06, 0.09.
- The curve enters the viewing window near −0.03 just above the horizontal axis and curves up to the right and reaches a maximum near 0.03.
- The curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.09.
(b)
What is the probability that the sample proportion will be within ±0.03 of the population proportion? (Round your answer to four decimal places.)
(c)
What is the probability that the sample proportion will be within ±0.05 of the population proportion? (Round your answer to four decimal places.)
(d)
What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
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