Question

Suppose that we are interested in learning about the level of fan support for the UNCG women's basketball team. We are considering different sampling strategies for choosing a sample of individuals to survey. From the following list select which strategies will most likely lead to an unbiased estimate of the overall fan support.

Group of answer choices

1. Survey the first 300 fans to arrive at the game.

2. Assume that the tickets are numbered on both ends with the same number. As the fans come in the door, we tear the ticket and place one half in a hat and once the game has started, we draw out 50 tickets at random and survey the holders of those tickets.

3. Select 500 fans who are wearing Blue and Gold

4. Survey the first 200 fans to leave the game.

5. Using a random number generator chose a sample of 100 fans from a list of ticket holders.

Answer 1

The type of estimate (biased or unbiased) for each of the 5 cases are analysed as follows.

1.

This will lead to a biased estimate.

In case we survey the first 300 fans to arrive at the game, all fans present in the ground are not equally likely to be selected in the sample. The fans who comes first (within first 300) are sure to be selected and those who comes later are excluded. So, there is clear bias in the selection procedure and so biased estimates will be obtained.

2.

This will lead to an unbiased estimate.

In this procedure, all fans coming to watch the game are equally likely to be selected as there is representative of each fan in terms of torn ticket in the hat and those torn tickets stored in the hat are later selected at random. So, there is no bias in the selection procedure and so unbiased estimates will be obtained.

3.

This will lead to a biased estimate.

In case we select 500 fans who are wearing blue and gold, all fans present in the ground are not equally likely to be selected in the sample. The fans who are wearing blue and gold will be selected and those who are not wearing blue or gold will be excluded. So, there is clear bias in the selection procedure and so biased estimates will be obtained.

4.

This will lead to a biased estimate.

In case we survey the first 200 fans to leave the ground, all fans present in the ground are not equally likely to be selected in the sample. The fans who leaves first (within first 200) are sure to be selected and those who leaves later are excluded. So, there is clear bias in the selection procedure and so biased estimates will be obtained.

5.

This will lead to an unbiased estimate.

In this procedure, all fans coming to watch the game are equally likely to be selected as we are using random number generator. Random number generator generates random numbers without any bias towards any value and so the sample of 100 fans using random number generator will be unbiased and so unbiased estimates will be obtained.