Question

12. In a poll taken in March of 2007, Gallup asked 1006 national adults whether they were
baseball fans. 36% said they were. A year previously 37% of a smaller sample had
reported being baseball fans.
a. Find and interpret a 90% confidence interval for the 2007 poll.
b. Would the margin of error be larger or smaller for a 99% confidence interval?
C. Find and interpret a 98% confidence interval.

Answer 1

The margin of error of the 90% confidence interval will be 0.024 and it increases when there's a higher confidence interval.

How to calculate the confidence interval?

The margin of error of the 99% confidence interval will be:

= 1.645 × [✓0.36(1 - 0.36)/1006

= 0.024

The margin of error for a 99% confidence interval will be calculated thus:

= 2.576 × [✓0.36(1 - 0.36)/1006

= 0.03898

This implies that margin error increases when there's a higher confidence interval.

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