Nancy is a waitress at Seventh Heaven Hamburgers. She wants to estimate the average amount each table leaves for a tip. A random sample of $5$ groups was taken and the amount they left for a tip $($in dollars$)$ is listed below:

$$12\mathrm{.}00$ $$6\mathrm{.}00$ $$7\mathrm{.}00$ $$5\mathrm{.}00$ $$5\mathrm{.}00$

a$.)$ Find a $90\%$ confidence interval for the average amount left by all groups. $(*$round to the nearest cent$*)$

$

$<$

$\backslash$mu

$<$

$

b$.)$ If the sample size were larger, with everything else remaining the same, would the margin of Error increase or decrease?

Decrease

Increase

c$.)$ If the Confidence level were $95\%$ instead of $90\%,$ would the range $($size$)$ of the Confidence Interval be larger or smaller?

Larger

Smaller