E Quest In a random survey of 207 self-employed individuals 21 reported having h

Question

E Quest In a random survey of 207 self-employed individuals 21 reported having had their tax retums audied by the RS in the past year Estimate the proposonof seremplyedidide wa in the past year. a) Check the assumptions and conditions for constructing a confidence interval b) Construct a confidence interval. c) Interpret your interval. context d) Explain what "98% confidence means in this a) Check the assumptions and conditions. Choose the correct answer below enough ne litaapeur te O A. This was a random sample of less than 10% of all sell employed tapayers there were at 10 successes and 10 failures sothe sample least O B. This was a random sample of more than 10% of all ser employedtaxpayers sample is too large the RS the audied by O C. The independence assumption is violated whether one person is to have his or her audited by allsalf employed taxpayers, there are less than 10 successes so the sample nor lage enough is O D. This was a random of less than 10% of answer boxes within your choice sample b) Select the correct choice below and, if necessary fill in the O A. The 98% confidence interval is e) are not satissed Round to one decimal place as needed) interval O B. The conditions for constructing a confidence below c) Interpret your interval select the comect answer Click to select your answer

Explanation / Answer

(a) Assumptions and conditions are met as per option (A)

(b)
pcap = 21/207 = 0.1015
For 98% CI, z-value = 2.33
lower bound = 0.1015 - 2.33*sqrt(0.1015*(1-0.1015)/207) = 0.0526
upper bound = 0.1015 + 2.33*sqrt(0.1015*(1-0.1015)/207) = 0.1504

Hence 98% CI = (5.3%, 15%)

(c) This CI shows that 98% is the probability that for a sample 207 self employeed individuals, proportion of individuals who have audited their tax returns will be within the range (5.3%, 15%).

Option (C)

(d) Option (A)

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