Q.18 - The Practice of Statistics for AP

Question

Predict the election Just before a presidential election, a national opinion poll increases the size of its weekly random sample from the usual $1500$ people to $4000$ people. 

(a) Does the larger random sample reduce the bias of the poll result? Explain. 

(b) Does it reduce the variability of the result? Explain 

Step-by-Step Solution

Answer

a). No, the larger random sample doesn't reduce the bias of the poll result.

b). Yes, it reduces the variability of the result.

Part (a) Step 1: Given Information

A national opinion poll increases the size of its weekly random sample from the usual $1500$ people to $4000$ people. 

Part (a) Step 2: Explanation

The bias will be unaffected if the sample size increases, because increasing the sample size does not affect the sampling techniques that were used.

Part (b) Step 1: Given Information

A national opinion poll increases the size of its weekly random sample from the usual $1500$ people to $4000$ people. 

Part (b) Step 2: Explanation

Yes, because if you have a larger sample, then you have more information about the distribution. This then allows you to make more accurate estimates and thus the variability will be reduced.