Question

A researcher is 95% confident that the interval from 5.2 hours to 7.8 hours captures u = the true mean amount of time

Answer 1

Answer: Choice B

No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.

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Explanation:

The greek letter mu is the population mean. It has the symbol $\mu$ which looks like the letter 'u' but with a tail at the front or left side.

The question is asking if mu = 5 is plausible if the researcher found the 95% confidence interval to be 5.2 < mu < 7.8

We see that 5 is not in that interval. It's a bit to the left of 5.2

Since mu = 5 is not in the interval, it's not a plausible value for the population mean.

Have we ruled it out with 100% confidence? No. Such a thing is not possible. There's always room for (slight) error. The researcher would need to do a census to be fully confident; however, such practices are very time consuming and expensive. This is the main reason why statistics is important to try to estimate the population with a sample.