In a survey of eating habits, 3800 adults were selected randomly and contacted by telephone. Respondents were asked, “Typically, how many times per week do you purchase food at a fast-food restaurant or convenience store?” On average, those surveyed purchased food at a fast-food restaurant or convenience store 2.4 times per week.
Suppose the researchers that conducted the survey described above decide to conduct it again, but will now interview only 2200 people. In the first survey, their sample average value was 2.4. Which of the following is true about the sample average value for the second survey?

Question

In a survey of eating habits, 3800 adults were selected randomly and contacted by telephone. Respondents were asked, “Typically, how many times per week do you purchase food at a fast-food restaurant or convenience store?” On average, those surveyed purchased food at a fast-food restaurant or convenience store 2.4 times per week.

Suppose the researchers that conducted the survey described above decide to conduct it again, but will now interview only 2200 people. In the first survey, their sample average value was 2.4. Which of the following is true about the sample average value for the second survey?

Accepted Answer

A different value for the sample average may result as sample averages are just estimates of the population value.

Answer

By the law of large numbers, it would again be 2.4.

Answer

By the law of large numbers, the smaller (second) survey will certainly produce a sample average farther from the true population average than the larger (first) survey.

Answer

The average income computed from the sample of 2200 people would be more accurate because smaller samples tend to be more homogeneous than larger samples.

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In a survey of eating habits, 3800 adults were selected randomly and contacted b...

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