9.12 Practice 1: single mean, known population standard deviation

Is this a test of means or proportions?

State the null and alternative hypotheses.

• a $H_o$ :
• b $H_a$ :

Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

What symbol represents the Random Variable for this test?

In words, define the Random Variable for this test.

Is the population standard deviation known and, if so, what is it?

Calculate the following:

• a $\overline{x}=$
• b $\sigma =$
• c $s_x=$
• d $n=$

Since both $\sigma$ and $s_x$ are given, which should be used? In 1 -2 complete sentences, explain why.

State the distribution to use for the hypothesis test.

Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized mean and the sample mean $\overline{x}$ . Shade the area corresponding to the p-value.

Find the p-value.

At a pre-conceived $\alpha =0\text{.}\text{05}$ , what is your:

• a Decision:
• b Reason for the decision:
• c Conclusion (write out in a complete sentence):

Does it appear that the mean jail time spent for first time convicted burglars has increased? Why or why not?