Question

# 3) People end up tossing 15% of what they buy at the grocery store. Assume this is the true population proportion

and that you plan to take a sample survey of 500 grocery shoppers to further investigate their behavior. a) Show the sampling distribution of “p bar”, the proportion of groceries thrown out by your sample respondents (calculate the mean and standard deviation). b) What is the probability that your survey will provide a sample proportion within ± .05 of the population proportion? c) What is the probability that your survey will provide a sample proportion within ± .025 of ￼￼￼the population proportion? 4) In 2010 the Better Business Bureau settled 80% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .80, the same as the overall proportion of complaints settled in 2010. a) Suppose you select a sample of 500 complaints involving new car dealers. Show the sampling distribution of “p bar”. (Calculate Mean and Standard Deviation) b) Based upon a sample of 500 complaints, what is the probability that the sample proportion will be within .05 of the population proportion? c) Suppose you select a sample of 250 complaints involving new car dealers. Show the sampling distribution of “p bar”. (Calculate Mean and Standard Deviation) d) Based upon the smaller sample of only 250 complaints, what is the probability that the sample proportion will be within .05 of the population proportion?

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