Chapter 1, Problem 28CP

UW Student survey In a University of Wisconsin (UW) study about alcohol abuse among students, 100 of the 40,858 members of the student body in Madison were sampled and asked to complete a questionnaire. One question asked was, “On how many days in the past week did you consume at least one alcoholic drink?”

1. a. Identify the population and the sample.
2. b. For the 40,858 students at UW, one characteristic of interest was the percentage who would respond “zero” to this question. For the 100 students sampled, suppose 29% gave this response. Does this mean that 29% of the entire population of UW students would make this response? Explain.
3. c. Is the numerical summary of 29% a sample statistic or a population parameter?

To determine

Identify the population and the sample.

Answer to Problem 28CP

The population is 40,858 members of the student body in Madison and the sample is 100 students who were asked to complete the questionnaire.

Explanation of Solution

The given information is that the out of 40,858 members, 100 students body in Madison were sampled and complete questionnaire is asked for the study of alcohol abuse among students. One of the question is asked in questionnaire was “On how many days in the past week did you consume at least one alcoholic drink ?”.

Population:

The total set of subjects of interest is termed as population.

Sample:

The subset of the population is termed as sample.

Here, it is observed that the 40,858 members of the student body in Madison represents the total set of subjects of interest. Therefore, the population is 40,858 members entire body in Madison. Also, it is observed that 100 students who were asked to complete the questionnaire are the subset of the population, 40,858 member of the student body in Madison.

Therefore, the sample is 100 students who were asked to complete the questionnaire.

To determine

Check whether the meaning of 29% of the entire population of UW students would make the given response or not. Also explain.

Explanation of Solution

Here, it is observed that the 29% is only an estimate of the percentage of all students who responded that zero for the given question “On how many days in the past week did you consume at least one alcoholic drink?”. Therefore, 29% gave response for 100 students do not mean that 29% of the entire population of UW students would make this response.

To determine

Check whether the numerical summary of 29% is a sample statistic or population statistic.

Answer to Problem 28CP

The numerical summary of 29% is a sample statistic.

Explanation of Solution

Statistics:

The statistics are the summary measures of the samples.

Parameter:

The parameters are the summary measures of the populations.

Here, it is observed that the numerical summary of 29%is the summaries of the sample ‘100 students who were asked to complete the questionnaire’. Therefore, the numerical summary of 29% is a sample statistic.