Question

6. The sampling distribution of the sample proportion Aa Aa In 2007, about 14% of new-car purchases in New York 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 New York can be viewed as an infinite population Define p as the proportion of the population of new-car purchases in New York 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 - .14 You will calculate an estimate of p by drawing a simple random sample of 50 new-car purchases made in New York. 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 simple 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 - .14.) Data Set Sample Variables 15 Simple random samples(n-50) drawn from a binomial population (p -0.14) Minitab was used to generate the samples. Samples Observations Observations 50 Variable v Type V Form V Values Missing Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Sample 11 Sample 12 Sample 13 Sample 14 Sample 15 Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric Qualitative Nonnumeric 50 50 50 50 50 50 50 50 50 Variables Observations> Variable Variable Variable Variable Correlation Correlation 50 50 50 50 Suppose you select sample 2. The values of Home Equity for sample 2 are in the tool in variable Sample 2. Use the sample proportion as an estimator for the population proportion p. The estimate is 26 . If the sample you select for your statistical study is one of the 1,000 samples we drew in our repeated sampling, the worst-luck sample you could draw is proportion. Use the tool to sort the observed values of p from least to greatest. That is, in the Data Set section of the tool under Observations, click the downward-pointing triangle directly below the Sample Proportion label. This will sort the sample proportions.) (Hint: The worst-luck sample is the sample whose sample proportion is farthest from the true population The mean of the sampling distribution of p is sampling is . The mean of the approximation of the sampling distribution obtained from repeated The standard deviation of the sampling distribution of p is obtained from repeated sampling is . The standard deviation of the approximation of the sampling distribution fall withirn Consider the the approximation of the sampling distribution obtained from repeated sampling. Of the sample proportions, one standard deviation of the mean, deviations of the mean. [Hint: Use the tool to filter for the desired sample proportions. That is, under the filter section of the Statistics page for the variable Sample Proportion, enter the appropriate values for Minimum and Maximum in their respective entry fields. Applying the filter will then allow you to obtain the number of values (located directly across from the Values label) that lie within the specified range.] fall within two standard deviations of the mean, and fall within three standard Examine the frequency histogram for the the approximation of the sampling distribution obtained from repeated sampling shown at right. A noral curve is superimposed on the histogram 180 160 140 120 Based on the histogram and your answers to the previous set of questions, the the approximation of the sampling distribution obtained from repeated sampling appears to be 60 40 20 0 0.02 0.08 0.26 0.32 0.14 Values of p-hat 0.20

Answer 1

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