A researcher conducted a survey to determine if people in a certain town prefer watching movies at the movie theatre or at home. The researcher asked 149 people who were at the mall on a Saturday. And nine of them refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the movie-watching preferences of all the people in the town? Is it A) the population size, B) the number of people who refused to respond, C) the sample size, or D) where the survey was conducted?
We were told in the question that the researcher asked 149 people. Therefore, we know the sample size. We were also told that they were asked in the mall on a Saturday. So we know where the survey was conducted. We were also told that nine of them refused to respond. We were not told in the question the population size of the town. This means that we can automatically rule out this option.
When conducting any survey, in order to be certain what the distribution of opinions are, you would need to ask everybody. And every person in the town would also need to respond. This should be incredibly expensive and time-consuming, especially for a trivial task like this. By taking a sample, we make the task a lot easier and cheaper. Generally, the more people you ask, the more likely you are to get a good idea of the distribution of opinions in the actual population.
In this survey, 140 of the 149 people answered the survey. This size sample is sufficiently large if it is well picked. Nine out of 149 people refused to respond. This is less than 10 percent so shouldn’t have a major impact on the reliability of the survey. When taking a sample, ideally, it needs to consist the people in the same proportions as the population as a whole, for example, ages, gender, income, and so on.
However, in this question, we haven’t been given any of this information. We were only told that they were asked in a shopping mall on Saturday. So we don’t know how representative the sample actually was. As we’ve restricted ourselves to only one location on one day, it is likely, although not certain, that we might not have a full representation of the full population. It is possible that the survey may be biased against people who prefer watching movies at home. This is because it seems possible or even likely that people who prefer to watch movies at home actually prefer being home at other times too. So they are less likely to be out in a shopping mall on a Saturday.
We can therefore conclude that the factor that makes it least likely that a reliable conclusion can be drawn is where the survey was conducted. In order to make the survey more accurate, we would need to ask on more occasions at different locations. This would hopefully give us a more representative sample of the whole population.