AP Statistics Confidence Intervals for a Proportion Quiz: 10 Questions with Explanations

A 0.12B 0.06C 0.50D 0.44

The margin of error is half the width: (0.56 – 0.44)/2 = 0.06.

A 19B 10C 5D 20

A 95% method captures the parameter about 95% of the time, which is about 19 of 20.

A the sample proportionB the critical value z* for 95% confidenceC the sample sizeD the standard error

z* = 1.96 leaves 2.5% in each tail of the standard normal curve.

A Increasing the confidence levelB Decreasing the sample sizeC Increasing the sample sizeD Using z* = 2.576

Larger n decreases the standard error and margin of error.

A There is a 95% chance that p is between 0.31 and 0.39B 95% of the sample lies within the intervalC 0.40 is not a plausible value for pD p-hat is 0.35 with no uncertainty

A claimed value outside the interval is not plausible at that confidence level. The other statements misinterpret the interval.

A n p-hat >= 10 and n(1 – p-hat) >= 10B n >= 30C p-hat >= 0.5D n p-hat <= 10

At least 10 successes and 10 failures are needed for a normal model.

A multiplied by 2B divided by 2C multiplied by sqrt(2)D multiplied by 4

ME is proportional to 1/sqrt(n).

A a narrower intervalB the same intervalC a smaller z*D a wider interval

Higher confidence requires a larger critical value and a larger margin of error.

A 0.24B 0.049C 0.4D 0.0024

sqrt(0.4(0.6)/100) = sqrt(0.0024) = 0.049.

A the sample was not randomB n is too largeC p-hat is too highD the confidence level is too low

Voluntary response samples are biased, so the interval formula does not apply.