Question

According to Reader's Digest, 41% of primary care doctors think their patients receive unnecessary medical care. Use z-table. a. Suppose a sample of 370 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. EP) .41 ор .0262 (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. .7498 c. What is the probability that the sample proportion will be within £0.05 of the population proportion. Round your answer to four decimals. .9356 d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would increase This is because the increase in the sample size makes the standard error, op , smaller

Answer 1

P= 0.41 (population proportion) a) n=370 E(P) =P P >0.41 P(1-P) op 10.41 (1-0,41) 2) 0,0256 h 370 -0.03< p < 0.41+0.03) b) P = sample proportion pl p-0.03 <p< P+0:03) = P(0.41-0 P(0.38 L P < 0.44) =P(0.38 -0.41 < P-4p(0.44 -0.41 =P(-1.1719 <2 21.1719) = 2P(012 21.1719) 0.0256 0.0256 = 2 * 0.3794 = 0.758 [From 2-table c) P(P-0.05< § <p +0.05) = P(0.36 < p <0.46) = P(0.36-0,41 PMP 20.46-0:41 0.0256 0.0256 ОР - P(-:1.9531 <z21.9531) = 2 Plo<2 2 1.9531) = 2*0,4746 = 0.9492 d) The probability would increase would increase. The is because the increase in the sample size make the standard error smaller.