8.6 Practice 2: confidence intervals for means, unknown population

Calculate the following:

• a $\overline{x}=$
• b $s_x=$
• c $n=$ $$

Define the Random Variable, $\overline{X}$ , in words. $\overline{X}=$ $\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

What is $\overline{x}$ estimating?

Is ${\sigma }_x$ known?

As a result of your answer to (4), state the exact distribution to use when calculating the Confidence Interval.

How much area is in both tails (combined)? $\alpha =$

How much area is in each tail? $\frac{\alpha }{2}=$

Calculate the following:

• a lower limit =
• b upper limit =
• c error bound =

The 95% Confidence Interval is:

Fill in the blanks on the graph with the areas, upper and lower limits of the Confidence Interval and the sample mean.

In one complete sentence, explain what the interval means.

Using the same $\overline{x}$ , $s_x$ , and level of confidence, suppose that $n$ were 69 instead of 39. Would the error bound become larger or smaller? How do you know?

Using the same $\overline{x}$ , $s_x$ , and $n=\text{39}$ , how would the error bound change if the confidence level were reduced to 90%? Why?