The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion. Use the information in the display to construct a 95% confidence interval for p.
A) (0.348, 0.652)
B) (0.285, 0.715)
C) (0.363, 0.637)
D) (0.337, 0.663)

Question

The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.  Use the information in the display to construct a 95% confidence interval for p.
A) (0.348, 0.652) 
B) (0.285, 0.715) 
C) (0.363, 0.637) 
D) (0.337, 0.663)

Quizplus · Accepted Answer

Since we want to construct a 95% confidence interval for p, which is a narrower interval than the 99% confidence interval given, we can use the conservative estimate of the standard error for p (sqrt[(0.5)(0.5)/n]). The lower bound of the 99% interval is 0.352 and the upper bound is 0.648. To find the corresponding 95% interval, we need to shift the bounds inward by multiplying the standard error by the z-score for a 95% confidence interval (1.96).

Lower bound: 0.352 - 1.96*sqrt[(0.5)(0.5)/n] 
Upper bound: 0.648 + 1.96*sqrt[(0.5)(0.5)/n]

Since n is not given, we cannot calculate the exact interval. However, we can see that the only choice that falls within this range is D, (0.337, 0.663).

The Following Display from a TI-84 Plus Calculator Presents a 99