SlackBoard, a company producing a Learning Management System $($LMS$),$ knows that their average user has

historically spent about $75$ minutes per day logged into their SlackBoard classes. They also know that time

spent logged in is approximately normally distributed. A recent random sample of $78$ accounts resulted in

an average time of $88$ logged in per day with a standard deviation of $65$ minutes per day.

Formulate and test a hypothesis to determine whether there is evidence to that there has been a change in

average individual use time per day. Conduct your test at a significance level of $=0\mathrm{.}1.$ Your hypotheses

are:

$H_0$:$=75$

$H_a$:$>75$

$H_0$:$=75$

$H_a$:$<mn\; id="EditorElement\_56889">7</mn><mn\; id="EditorElement\_56890">5</mn>$

$H_0$:$=0$

$H_a$:$>0$

$H_0$:$=75$

$H_a$:$75$

What is the test statistic for this test?

test statistic $=$

$($Report answer accurate to $2$ decimal places.$)$

What is the $p-$value for this test?

p$-$value $=$

$($Report answer accurate to $4$ decimal places.$)$

The decision reached is

Reject $H_0$ and accept $H_a$

Fail to reject $H_0$

As such, the final conclusion is that

There is significant evidence to suggest a changed average usage time per user.

There is significant evidence that suggests no change in average usage.

The usage times have not changed.

There is not significant evidence to suggest a changed average usage time per user.