A simple random sample of 200 married people were asked the question, \"Would yo

Question

A simple random sample of 200 married people were asked the question, "Would you remarry your spouse a second time if you were given the chance?" Based on the 200 responses, a 95% confidence interval for the proportion of people who reported they would remarry their spouse is (.812,.908). Which of the following is the correct interpretation of the confidence interval? The probability that 95% of people would remarry their spouse is between .812 and .908. 95% of all confidence intervals calculated regarding the proportion of people who would remarry their spouse a second time will contain the sample proportion of .86. We are 95% confident that between 81.2% and 90.8% of the next 200 married people surveyed would be willing to remarry their spouse. We are 95% confident that the true proportion of people who would remarry their spouse is between 81.2% and 90.8%. QUESTION 2 If the sample proportion had been .90 instead of .86 as observed in the original poll while still using a sample size of 200 and a 95% confidence interval, then the confidence interval would have been: The same width Narrower Wider

Explanation / Answer

1) Given that, 95% confidence interval for the proportion of people who reported they would remarry their spouse is (0.812, 0.908)

Interpretation of this result is,

We are 95% confident that the true proportion of people who would remarry their spouse is between 81.2% and 90.8%

2) If the sample proportion had been 0.90 instead of 0.86 as observed in the original poll while using a sample size of 200 and 95% confidence interval, then the confidence interval would have been Narrower

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