Chapter 7

In your own words, explain what the null hypothesis is.

What are Type I and Type II Errors?

Why do we phrase null and alternative hypotheses with population parameters and not sample means?

If our null hypothesis is \({ }^{4} H_{0}: \mu=40^{\prime \prime}\), what are the three possible alternative hypotheses?

Why do we state our hypotheses and decision criteria before we collect our data?

Determine whether you would reject or fail to reject the null hypothesis in the following situations: a. \(z=1.99\), two-tailed test at \(\alpha=0.05\) b. \(z=0.34, z *=1.645\) c. \(p=0.03, \alpha=0.05\) d. \(p=0.015, \alpha=0.01\)

You get hired as a server at a local restaurant, and the manager tells you that servers' tips are $$\$ 42$$ on average but vary about $$\$ 12(\mu=42, \sigma=12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don't know if you will make more or less in tips. After working 16 shifts. you find that your average nightly amount is $$\$ 44.50$$ from tips. Test for a difference between this value and the population mean at the \(\alpha=0.05\) level of significance.