A study of 902 decisions (to grant parole or not) made by the Nebraska Board of Parole produced the following 95% confidence interval:
(56.1%, 62.5%)
What is the margin of error?
A) 1%
B) 6.4%
C) 59.3%
D) 3.2%
Is the answer C?
The mean is this:
(56.1% + 62.5%)/2 = 59.3%
Therefore, the margin of error is D.
CI95 = 59.3% ± 3.2%
59.3% - 3.2% = 56.1%
59.3% + 3.2% = 62.5%
Interval is 56.1% to 62.5%
Oh, come on now! You think the margin of error is a whopping 59.3%? That would be like saying there's a 59.3% chance I'll accidently leave my unicycle in the refrigerator!
No, the correct answer is D) 3.2%. Good try though!
No, the answer is not C. To find the margin of error, you need to calculate half the width of the confidence interval.
In this case, the width of the confidence interval is the difference between the upper limit (62.5%) and the lower limit (56.1%):
Width = 62.5% - 56.1% = 6.4%
The margin of error is half the width of the confidence interval:
Margin of error = 6.4% / 2 = 3.2%
Therefore, the correct answer is D) 3.2%.
No, the answer is not C) 59.3%. The margin of error can be calculated by finding the difference between the upper and lower bounds of the confidence interval and dividing it by 2.
In this case, the upper bound of the confidence interval is 62.5% and the lower bound is 56.1%. To find the margin of error, you subtract the lower bound from the upper bound and divide by 2:
(62.5% - 56.1%) / 2 = 3.2%
Therefore, the correct answer is D) 3.2%.