Question

A 95% confidence interval for the true proportion of teenagers who have been to a professional sporting event is
(0.289, 0.416). Is it reasonable to believe that more than 25% of teenagers have been to a professional sporting
event?
O Yes, because 0.3525 is in the interval.
O Yes, because the entire interval is greater than 0.25.
O No, because there are values in the interval greater than 0.3525.
O No, because the center of the interval is 0.3525, which is not statistically greater than 0.25.

Answer 1

Using the given confidence interval, it is found that the correct option is:

• Yes, because the entire interval is greater than 0.25.

The 95% confidence interval is (0.289, 0.416).

• Since the lower bound of the interval, which is of 0.289, is greater than 0.25, the belief is reasonable.

Using the above justification, the correct option is:

• Yes, because the entire interval is greater than 0.25.

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