A researcher is studying how many hours per day people are staying at home during the COVID-19 pandemic. Suppose he obtains a list of all residential addresses in a town and then randomly selects 100 of these. He goes door-to-door during the day and knocks or rings the doorbell. If someone answers the door, he asks them to estimate how many hours per day they have been home during the past week. If no one answers the door, he moves on to the next house on the list. He then averages all the numbers obtained to try to estimate the average time at home in the whole town.

(a) The researcher took a random sample of households. Are the people he talks to like a random sample of all the people in the town? Considering specifically the variable he is interested in studying, in what way are the people he talks to likely to be different from the townspeople in general?

(b) Will the researcher's average tend to be too high, too low, or about right? Explain.

The researcher's sample is unlikely to represent the entire population due to inherent biases in his method and leading to a higher average than the actual average of the town's residents.

The researcher's approach does not provide a truly random sample of the population in the context of the variable being studied. The people who answer the door during the day are likely to be those who spend more time at home, either due to work-from-home policies, unemployment, retirement, or other factors that keep them at home during daytime hours.

This sample thus may not represent the average townspeople who might be at work, school, or other engagements during the day.

As for the resulting data, if the researcher depends only on the answers obtained from this skewed sample, the average number of hours they calculate people stay at home is likely to be higher than the real average for the whole town because they are talking to a concentration of people who are home during the day.

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