Question

select the correct answer.

a company is analyzing whether its employees prefer to skip their lunch break and leave a half-hour early each day or take a lunch break and leave at the normal time each day. it conducts an observational study to determine which option is selected more often. at the end of the first week, the company finds that the majority of employees prefer to skip their lunch break and leave a half-hour early each day.

the company then repeats the observational study for 10 more weeks. the study yields the same results for only five of the weeks. what generalization can be made from the results of this study?

• the majority of employees prefer to take a lunch break and leave at the normal time each day.
• the majority of employees prefer to skip their lunch break and leave a half-hour early.
• the results are inconclusive; therefore a generalization cannot be made regarding which option is selected more often.
• the sample is biased; therefore, a generalization cannot be made regarding which option is selected more often.

Explanation:

Analyze the study design

The company is conducting an observational study to determine employee preferences regarding lunch breaks. In the first week, the majority preferred skipping lunch to leave early. However, when repeated for 10 more weeks, this result only occurred in 5 of those weeks.

Evaluate the consistency of results

Using the Statistical Generalization knowledge point, we look for consistent patterns to make a reliable claim. Out of 11 total weeks of observation, the majority preferred leaving early in only 6 weeks (the first week plus 5 of the subsequent 10 weeks). This is approximately half of the time (\(54.5\%\)).

Determine the validity of generalizations

Because the results are highly variable and split almost evenly between the two options across the 11 weeks, there is no clear, consistent majority preference.

Assess the multiple-choice options

• Option 1 claims a majority prefer taking a normal lunch, which is unsupported.
• Option 2 claims a majority prefer skipping lunch, which is also unsupported given the inconsistent weekly results.
• Option 3 correctly identifies that the inconsistent results make the study inconclusive, meaning a reliable generalization cannot be made.
• Option 4 claims the sample is biased, but there is no evidence of sampling bias in how the observational study was conducted.

Answer:

• (A) The majority of employees prefer to take a lunch break and leave at the normal time each day.
• (B) The majority of employees prefer to skip their lunch break and leave a half-hour early.
• (C) The results are inconclusive; therefore a generalization cannot be made regarding which option is selected more often. (Correct answer)
• (D) The sample is biased; therefore, a generalization cannot be made regarding which option is selected more often.