Question

the hamden board of education wants to know how the community feels about building a new media center for the middle school. they called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. which of the following are true of the sample of 40 voters? check all that apply.
the sample is not randomly chosen.
the sample should be larger to give more reliable information.
the sample size is too large to make inferences.
the sample size is too small to represent the population.
the sample size is too small and will show larger variation.
the sample is invalid because it randomly chooses voters.
the sample size is too small and can lead to false inferences.

Explanation:

1. Regarding "The sample is not randomly chosen": The method of calling every tenth person (systematic sampling) is a type of random sampling (if the list is random), so this is false.
2. Regarding "The sample should be larger to give more reliable information": Larger samples generally reduce sampling error and give more reliable results, so this is true.
3. Regarding "The sample size is too large to make inferences": A sample size of 40 from 7300 is small, not too large, so this is false.
4. Regarding "The sample size is too small to represent the population": With a population of 7300, a sample of 40 is relatively small and may not fully represent the population, so this is true.
5. Regarding "The sample size is too small and will show larger variation": Smaller samples have more variability in their statistics (e.g., sample proportions/means) compared to larger samples, so this is true.
6. Regarding "The sample is invalid because it randomly chooses voters": Random sampling is a valid method, so this is false.
7. Regarding "The sample size is too small and can lead to false inferences": Small samples have a higher chance of not reflecting the true population characteristics, leading to false inferences, so this is true.

Answer:

• The sample should be larger to give more reliable information.
• The sample size is too small to represent the population.
• The sample size is too small and will show larger variation.
• The sample size is too small and can lead to false inferences.