Question

Answer true or false to the following statement, and give a reason for your answer: If a $95\%$ confidence interval for a population mean. $\mathit{\mu }$, is from $33.8$ to $39.0$, the mean of the population must lie somewhere between $33.8$ and $39.0$

Short answer

False.

Step-by-step solution

Explanation

The stated assertion is incorrect.

We can argue that we are$95\%$ certain that $\mu$ resides somewhere between $33.8$ and $39$ based on the $95\%$ confidence interval, $(33.8,39)$ of the population mean $\mu$That is to say, the population means may or may not be within the interval, but we are $95\%$ sure that it does.