In a random survey of 214 self-employed individuals, 15 reported having had thei

Question

In a random survey of 214 self-employed individuals, 15 reported having had their tax return audited by the IRS in the past year. Estimate the proportion of self-employed individuals nationwide who've been audited by the IRS in the past year. a) Check the assumptions and conditions for constructing a confidence interval. b) Construct a 98% confidence interval. c) Interpret your interval. d) Explain what "98% confidence" means in this context. a) Check the assumptions and conditions Choose the correct answer below. A. This was a random sample of more than 10% of all self-employed taxpayers, the sample is too large. B. The independence assumption is violated: whether one person is "less likely" to have his or her tax returns audited by the IRS is dependent on whether another person is "less likely" to have his or her tax returns audited by the IRS. C. This was a random sample of less than 10% of all self-employed taxpayers: there were at least 10 successes and 10 failures, so the sample is large enough. The data appear to be independent. D. This was a random sample of less than 10% of all self-employed taxpayers: there are less than 10 successes, so the sample is not large enough. b) Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The 98% confidence interval is (%, %). B. The conditions for constructing a confidence interval are not satisfied.

Explanation / Answer

Total number of sample size = n =214

total number of success = 15

So the proportion of success = 15/214 = 0.07 < 0.10

So the estimated proportion = 0.07

a) Since the number of success = 7% less that 10%

So the correct choice is d)

b) Since the assumption of number of successes are at least 10 is not satisfied so we can not used normal approximation to find the confidence interval for true proportion using the small sample size.

So correct option is B)

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