Question

3. The sampling distribution of the sample proportion Aa Aa In 2007, about 20% of new-car purchases in Florida were financed with a home equity loan. [Source: "Auto Industry Feels the Pain of Tight Credit," The New York Times, May 27, 2008.] The ongoing process of new-car purchases in Florida can be viewed as an infinite population. Define p as the proportion of the population of new-car purchases in Florida that are financed with a home equity loan. The true population value of p is not known, but for the sake of this exercise assume that p -.20 You will calculate an estimate of p by drawing a random sample of 50 new-car purchases made in Florida. If the purchase was financed with a home equity loan, you record a value of Yes for the variable Home Equity. If the purchase was not financed with a home equity loan, you record a value of No for the variable Home Equity Since the population is infinite, an infinite number of samples can be drawn from the population. The sample data for the variable Home Equity for 15 random samples (of size n-50) that could be pulled from the population are in the data set samples. (Each value of Home Equity is a random selection from a binomial population with p .20.) Data Set Samples Sample 3 Variable Sample 3 Qualitative/Nonnumeric Sample 3 Observations 50 Missing 0 Values50 Full Data Set IncludeFrequency Relative Frency Relative 0.260 0.740 1.000 Filter Filtered Data Category 13 0.260 37 0.740 50 1.000 13 Bar C 37 Total Variable Variable Variable Correlation Correlation Sample 9 Suppose you select sample 3. The values of Home Equity for sample 3 are in the tool in variable Sample 3. Use the sample proportion as an estimator for the population proportion p. The point estimate is Now suppose that instead of sample 3, you pull sample 9. Then your point estimate of p is Data Set Variable Variable Samples Sample 3 Sample 9 Sample 9 Qualitative/Nonnumeric Sample 9 Observations 50 Missing0 Values50 Full Data Set IncludeFrequency Relative Frency Relative 6 0.120 0.880 Filter Filtered Data Category 6 0.120 0.880 Total 1.000 1.000 Variable Variable Correlation Correlation

Answer 1

for sample 3 point estimate of p is x/n = 13/50 = 0.26

for sample 9 , point estimate is 6/50 = 0.12

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