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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 $16,407. Assume that the standard deviation is a" = $2950. Use ztable. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $237 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 .3400 n = 50 .4314 n = 100 .5762 n = 400 .8962 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 the probability that the sample mean will be within a specified distance of the population mean. In this instance, the probability of being within i237 of ,u ranges from .3400 for a sample of size 30 to .8926 for a sample of size 400. 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 $16,407. Assume that the standard deviation is 0' = $2950. Use ztable. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $237 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 .3400 n = 50 .4314 n = 100 .5762 n = 400 .8962 b. What is the .' nple size when attempting to estimate the population mean? Round your answers to four decimals. - Select your answer - A larger sample a the probability that the sample mean will be within a specified distance of the population mean. In this instance, the probability of b decreases nges from .3400 for a sample of size 30 to .8926 for a sample of size 400. According to Reader's Digest, 35% of primary care doctors think their patients receive unnecessary medical care. Use the ztable. 3. Suppose a sample of 360 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. ECU?) = (to 2 decimals) 01-, = .0251 (to 4 decimals) b. What is the probability that the sample proportion will be within :l:0.03 of the population proportion? Round your answer to four decimals. .8849 c. What is the probability that the sample proportion will be within :l:0.05 of the population proportion? Round your answer to four decimals. .9767 d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would . This is because the increase in the sample size makes the standard error, 0;, . According to Reader's Digest, 35% of primary care doctors think their patients receive unnecessary medical care. Use the ztable. a. Suppose a sample of 360 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. ECU?) = (to 2 decimals) Cr; 2 .0251 (to 4 decimals) b. What is the probability that the sample proportion will be within :i:0.03 of the population proportion? Round your answer to four decimals. .8849 c. What is the probability that the sample proportion will be within :i:0.05 of the population proportion? Round your answer to four decimals. .9767 d. What would be the: 'ample on the probabilities in parts (b) and (c)? Why? Select your answer The probabilities woulc :] . This is because the increase in the sample size makes the standard error, 0;, . decrease According to Reader's Digest, 35% of primary care doctors think their patients receive unnecessary medical care. Use the ztable. a. Suppose a sample of 360 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. ECU?) = (to 2 decimals) Cr; 2 .0251 (to 4 decimals) b. What is the probability that the sample proportion will be within :l:0.03 of the population proportion? Round your answer to four decimals. .8849 c. What is the probability that the sample proportion will be within :l:0.05 of the population proportion? Round your answer to four decimals. .9767 - Select your answer - d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? I arger The probabilities would . This is because the increase in the sample size makes the standard error, a; j. A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 nished products and computes the sample mean product weight 5. If test results over a long period of time show that 5% of the E values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? Use ztable. Mean .06 (to 1 decimal) Standard deviation .33 (to 2 decimals) Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News 8: World Report website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Answer the following questions about the cost of automobile repairs. 3. What is the probability that the cost will be more than $450 (to four decimals)? .1728 b. What is the probability that the cost will be less than $250 (to four decimals)? .0918 c. What is the probability that the cost will be between $250 and $450 (to four decimals)? .7346 d. If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost (to two decimals)? $ 222.24 Suppose that the mean daily viewing time of television is 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. 3. What is the probability that a household views television between 3 and 9 hours a day (to 4 decimals)? .5864 b. How many hours of television viewing must a household have in order to be in the top 4% of all television viewing households (to 2 decimals)? 12.73 hours c. What is the probability that a household views television more than 2 hours a day (to 4 decimals)? .945 Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraudthe practice of someone clicking on an ad solely for the purpose of driving up advertising revenuehas become a problem. According to BusinessWeek, 42% of advertisers claim they have been a victim of click fraud. Suppose a simple random sample of 280 advertisers will be taken to learn more about how they are affected by this practice. Use ztable. a. What is the probability that the sample proportion will be within ::0.05 of the population proportion experiencing click fraud? .8886 (to 4 decimals) b. What is the probability that the sample proportion will be greater than 0.48? .0192 (to 4 decimals) The Economic Policy Institute periodically issues reports on worker's wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. Use ztable. Round your answers to four decimal places. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? .8764 b. What is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean, $27.83? .9146 c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? Why? Because the standard error for female graduates is the standard error for male graduates d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.60 below the population mean, $27.83? .0548 The Economic Policy Institute periodically issues reports on worker's wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. Use ztable. Round your answers to four decimal places. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? .8764 b. What is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean, $27.83? .9146 'ding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population Select your answer Part (a) _a Why? Because the standard error for female graduates is the standard error for male graduates d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.60 below the population mean, $27.83? .0548 The Economic Policy Institute periodically issues reports on worker's wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. Use ztable. Round your answers to four decimal places. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? .8764 b. What is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean, $27.83? .9146 c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? Part (b) v Select your answer Why? equal to Because the standard error for female graduates is J smaller than athe standard error for male graduates greater than (I. What is the probability that a sample of 120 fen le a sample mean more than $0.60 below the population mean, $27.83? .0548