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A sample median of 1,005 visitors would be most likely to occur for the sample size given by: Option A: 20
What does median behave like for large sample?
As the value of n (the sample size) grows larger, the sampling distribution tends to being normal. For an approximate normal distribution, its mean, median, and mode all are approx coincident. And as the sample size increases, the sample mean tends to being the population mean as per the weak law of large numbers. For n > 30, we can approximate it using normal distribution usually.
We're given that:
- Population median (the real median of the number of visitors to the zoo) = 893
- We want to choose value of n from 20, 75,, 300, 500, 1000 for which the sample median would be 1005.
So, as we know, as the sample size increases, the sample mean and sample median and sample mode, all will tend to the population mean, median and mode (assuming population is large enough that they're all same).
Thus, the smaller the sample size, the more likely it is for holding 1005 as sample median instead of approx 893.
So, size 20 is most likely to have that median as it is the smallest sample size given.
Thus, a sample median of 1,005 visitors would be most likely to occur for the sample size given by: Option A: 20
Learn more about weak law of large numbers here:
https://brainly.com/question/9061041
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