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Find the 95% confidence interval for the population proportion, p, when n = 28 and x = 12. Use your calculator memory function to store the p-hat value, or use 5 or 6 places of decimal if you are entering the p-hat value in the formula. Enter only the LOWER boundary of your interval as your answer, rounded to 3 places of decimal.
CAUTION: A very common error in this question is to think because n = 28 that we will be using the t-distribution. This is NOT the case. We ONLY use the t-distribution when we are dealing with means. And it is true that IF we were dealing with means and n = 28 and the underlying population was normally distributed, then we would be using the t-distribution. But in this question we are dealing with proportion, and the question we must ask ourselves is not "is n thirty or more?", but: "are we expecting at least 5 successes and at least 5 failures?"
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