There is interest in learning about the number of internet connected devices tha

Question

There is interest in learning about the number of internet connected devices that people own. You conduct a poll of 100 randomly selected adults from across the country and ask them how many internet connect devices they own (smartphones computers, tablets, smart tvs, etc). The Gallup Poll also conducts a poll of 1010 randomly selected adults from across the country and asks the same question. Which survey is more likely to report that the mean number of internet-connected devices is below 2.4, assuming that the actual mean is 3.6? Explain. Hint: You do NOT need to calculate anything for this problem. Assume that non-response and undercoverage are not an issue with the polling.

Explanation / Answer

The sample of size 100 is more likely to report that mean is below 2.4.

Explanation: The smaller the sample size, the less accurate estimation. In fact if the sample size is equal to the population, the estimation will be perfect. If the sample size is too small relative to the population, its too likely to overestimate or underestimate the statistic. Supose we want to estimate the average score of a class of 100 students. for this purpose, we select a sample of 2 students. It is very clear that these two sample would rarely estimate the average score.  

Here in this problem, though the sample of size 1010 doesnot also seem to be adequate for a country, but it will definitely be better that the sample of size 100. Thus the conclusion.

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