True or false: For Questions 1 to 10, assume a 95% confidence interval has been

Question

True or false:

For Questions 1 to 10, assume a 95% confidence interval has been calculated for the proportion of orange M&Ms; from a bag of 121 M&Ms.; The interval is (0.32,0.49). Forty-nine were orange. True or false: If this method were used to generate an interval estimate over and over again with different samples, in the long run, 95% of the resulting intervals would capture the true value of the characteristic being estimated True False There is a 95% chance that the true proportion lies between 0.32 and 0.49. True False 95% of the time, the true proportion will lie between 0.32 and 0 49. True False

Explanation / Answer

Question1: The statement is true. By the definition of confidence interval, it means that if we generate the intervals again and again, 95% of those intervals will contain the true value of the characteristic being estimated.

Question2:This statement is false. Confidence interval doesn't mean that there is a 95% chance of the actual value to lie in that interval. As stated it just means that 95% of the time the actual value will fall between this range.

Question3: This statement is true. Since we have 95% confidence interval, it means that 95% of the times, the actual value will fall wihtin the given range.

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