Question

Describe the relationship between bias and variability through an example. Given that the proportion of all Americans that believe President Bush is doing a good job is 42%, you then conduct a series of 10 polls to confirm or refute this claim of 42%. Describe your results if:a) There is high bias and high variability in your results. b) There is high bias and low variability in your results. c) There is low bias and high variability in your results. d) There is low bias and low variability in your results.

Answer 1

Answer:

a. High bias, High variability : the claim is not true. 42% not accepted

b. High bias, Low variability : 42% claim is not accepted.

c. Low bias, High variability : 42% claim will have been true if the sampling distribution is used is consistent. but the claim is not true because the 10 polls sample are not of the same group.

 d. Low bias, Low variability: the claim is very true. 42% is accepted

Step-by-step explanation:

A high variability means that the statistics within the sample distribution are very inconsistent with each other.

While a low variability means that the statistics within the sample distribution are very consistent with each other.

High bias occurs whenever the mean of the sampling distribution is FAR from the mean of the parameter being measured.

While low bias indicates that the mean of the sampling distribution is CLOSE to the parameter being measured.

A biased estimator is when the mean of the sampling distribution is not equal to the true value of the parameter being estimated

Unbiased estimator is when the mean of the sampling distribution is equal to the true value of the parameter getting estimated

Given that the proportion of all Americans that believe President Bush is doing a good job is 42%, you then conduct a series of 10 polls to confirm or refute this claim of 42%. using Sampling Variability ;

b. High bias, Low variability : 42% claim is not accepted.

c. Low bias, High variability : 42% claim will have been true if the sampling distribution is used is consistent. but the claim is not true because the 10 polls sample are not of the same group.

a. High bias, High variability : the claim is not true. 42% not accepted

d. Low bias, Low variability: the claim is very true. 42% is accepted

Reference from https://prezi.com/zhnqdnqhwnnd/ap-statistics/

Answer 2

Answer:

Answers explained below

Step-by-step explanation:

(a) If there is high bias and high variability, the numbers will not be anywhere near the 42 percent value. If I wrote down 10 numbers and they were all completely different from 42, I would know that I have high bias and high variability.

(b) If a certain number of polls have just about the same average, but are nowhere near 42 percent, they have high bias and low variability. For example, 20 percent, but its far from 42 percent.

(c) If there is low bias and high variability, if you list the polls they will have an average around 42 percent. If you average the polls, you'll get 42 percent low bias. The high variability might be 20, 72% 42% 63% 10%

(d) If there is low bias and low variability, all of the polls will be close to 42 percent.