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

Short 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.

Step-by-step solution

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.