According to Reader's Digest, 40%% of primary care doctors think their patients receive unnecessary medical care. Use z-table. a. Suppose a sample of 350 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) = 0.32 OF (to 4 decimals) b. What is the probability that the sample proportion will be within 10.03 of the population proportion. Round your answer to four decimals. c. What is the probability that the sample proportion will be within 10.05 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 | increase . This is because the increase in the sample size makes the standard error, Up , smaller VO. The Wall Street Journal reported that 33%% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,019. Assume that the standard deviation is = $2,509. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $180 of the population mean for each of the following sample sizes: 30, 50, 100, and 4007 Round your answers to four decimals. 1 = 30 0.3050 1 = 50 X n = 100 n = 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample | increases the probability that the sample mean will be within a specified distance of the population mean, In the automobile insurance example, the probability of being within 1:180 of / ranges from 0.3050 3 for a sample of size 30 to for a sample of size 400