A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed in regards to news from other countries. A standardized test is used to assess student$$s knowledge of world events $($national reported mean$=65).$ A sample of $30$ students are tested $($sample mean$=58,$ sample standard deviation $=3\mathrm{.}2).$

Compute a $99$ percent confidence interval based on this sample data.

a$)$ Not enough data

b$)[58,65]$

c$)[54\mathrm{.}8,62\mathrm{.}5]$

d$)[56\mathrm{.}5,59\mathrm{.}5]$

What is the margin of error?

a$)1\mathrm{.}5$

b$)99\%$

c$)3\mathrm{.}0$

d$)$ Not enough data

How do these students compare to the national sample?

a$)$ Above the national mean

b$)$ Below the national mean

c$)$ Around the national mean

d$)$ Not enough data

What is the minimum sample that the university have to take if they wanted to create a $99\%$ confidence interval with a margin of error of $5$ points?

a$)2\mathrm{.}72$

b$)3\mathrm{.}0$

c$)30$

d$)192$