Question

A survey was run on Facebook to determine if people had tested positive for COVID-19. There were 14,000 San Diego residents who responded and their infection rate was found to be 9%. Another simple random survey was done of 2,000 San Diego residents and it was found that 5% of them had been infected. Based on your knowledge of statistics, what do you tell the County Health Officer about which results to believe?

a) The rate is probably close to 9%. The first survey has a a much larger sample size so its results are likely to be more accurate.

b) The true infection rate is actually 8.5%. This is found by combining both surveys and doing the math.

c) The rate is probably close to 7%. The best thing to do would be to average them since both surveys are valid surveys.

d) The rate is probably close to 5%. The second survey is the only one that any statistical conclusion can be drawn from.

Answer 1

Answer: Option (d) is correct.

Explanation

The survey which was run on facebook does not represent the population of San Diego. The sample is not randomly selected. Hence, even though the number of responses is higher, it should not be considered for statistical analysis.

On the other hand, a simple random survey is a good representation of population.

Therefore, the rate is probably close to 5% (the result of second survey which is the simple random survey). The second survey is the only one that any statistical conclusion can be drawn from.

Hence, option (d) is correct.