Mean hypothesis testing with tdistribution  Hypothesis Testing
Mean hypothesis testing with tdistribution
Lessons
Notes:
If $\sigma$ is not known, then we cannot use the test statistic:
$Z=\frac{\overline{x}\mu}{\frac{\sigma}{\sqrt{n}}}$
We will instead use the teststatistic:
$Z=\frac{\overline{x}\mu}{\frac{s}{\sqrt{n}}}$
So at the very least we must know the sample standard deviation, $s$.
Furthermore we will be using a tdistribution instead of our standard normal distribution to find our fail to reject region and our rejection region.

2.
“Redline motorcycles” is a company that fixes and tunes motorcycles. A sample of 75 of their motorcycles had an average of 135hp, and a standard deviation of 35hp. Test the following claims with a 99% confidence level: