Chapter 11.3, Problem 34E

(a)

To determine

To identify: the type of sample described.

Answer to Problem 34E

Here, the state is divided into small groups (33 counties) and the sample of 50 voters is then randomly selected from each group. So, this sample is a stratified sample.

Explanation of Solution

Given:

  

Calculation:

In this case a poll is conducted to predict results of a statewide election. For that, 50 voters in each of the state’s 33 counties were surveyed.

Since, state is divided into small groups (33 counties) and the sample of 50 voters is then randomly selected from each group. Thus, this sample is a stratified sample.

Conclusion:

Hence, the state is divided into small groups (33 counties) and the sample of 50 voters is then randomly selected from each group. So, this sample is a stratified sample.

(b)

To determine

To explain: how the diagram results a biased sample..

Answer to Problem 34E

Each county has the same sampling fraction. In this way a sample will be selected that is more representative of the population.

Explanation of Solution

Calculation:

The results of this polling method could be biased.

From the diagram, it is clear that the number of voters in each country is different.

The size of the sample in each country should be taken in proportion to the population of the county. This will ensure that each county has the same sampling fraction. In this way a sample will be selected that is more representative of the population.

Conclusion:

Hence, each county has the same sampling fraction. In this way a sample will be selected that is more representative of the population.