You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.02}$.

      $\displaystyle {H}_{{o}}:\mu={83.5}$
      $\displaystyle {H}_{{a}}:\mu<{83.5}$

You believe the population is normally distributed and you know the standard deviation is $\displaystyle \sigma={6.8}$. You obtain a sample mean of $\displaystyle {M}={82.6}$ for a sample of size $\displaystyle {n}={34}$.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

This test statistic leads to a decision to...

As such, the final conclusion is that...