Would it be unusual for the mean of a sample of 3 to be 115 or more?
hint: what does small sample size tell you about the standard deviation or variance (is it small or large?)?
To determine whether it would be unusual for the mean of a sample of 3 to be 115 or more, you can use the concept of sampling distributions and statistical inference.
1. First, gather a sample of size 3 from the population you are interested in.
2. Calculate the mean of the sample.
3. Repeat steps 1 and 2 many times to create a sampling distribution of the means.
4. Analyze the sampling distribution to determine the probability of obtaining a mean of 115 or more.
5. If the probability is low (typically less than 0.05 or 5%), then it can be considered unusual.
However, if you do not have access to the population data or the ability to create a sampling distribution, you can still gain some insight.
Consider the context of the data you are working with. For example, if you are sampling the heights of adult females, it is unlikely that a sample mean of 115 or more would be possible, as it would imply a relatively extreme height.
In general, the more extreme the sample mean is in relation to the variability of the population, the more unusual it is likely to be.
Remember, statistical inference provides estimates and probabilities, but it cannot definitively determine whether something is unusual or not.