A recent Gallup poll showed the president’s approval rating at 60%. Some friends

Question

A recent Gallup poll showed the president’s approval rating at 60%. Some friends use this information (along with the sample size from the poll) and find theory-based confidence intervals for the proportion of all adult Americans that approve of the presidents approve of the president's performance. Of the following four confidence intervals, identify the ones that were definitely done incorrectly. (There may be more than one interval that is incorrect.)

a. (0.58, 0.62)

b. (0.47, 0.53)

c. (0.60, 0.66)

d. (0.57, 0.63)

Explanation / Answer

For any interval to be correct, the midpoint of the interval should always be sample proportion which in this case is 0.60.

Hence,

a) Midpoint = (0.58 + 0.62)/2 = 0.60; Correct

b) Midpoint = (0.47 + 0.53)/2 = 0.50; Incorrect

c) Midpoint = (0.60 + 0.66)/2 = 0.63; Incorrect

d) Midpoint = (0.57 + 0.63)/2 = 0.60; Correct

Hence,

Part b and part c are definitely incorrect.

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