The time between eruptions of "Old Faithful" geyser in Yellowstone National Park is random, but is related to the duration of the last eruption. The table below shows the times for a random sample of 10 eruptions.

1. What is the correlation between duration and the time to the next eruption?

2. What is the regression equation for predicting time to the next eruption from the duration of an eruption?

3. You just missed an eruption. The sign at the geyser says "Next Eruption in 50 minutes." Can you tell me what the duration of the previous eruption was in minutes? Explain why you can or why you cannot do this.

4. Suppose the park ranger tells you the eruption you just missed lasted 3 minutes. How long must you wait around to see the next eruption?

Suppose the hourly wage for American workers is normally distributed with an average of $12.98 with a standard deviation of $5.21.

5. What percentage of American workers earn more than $20 per hour?

6. A simple random sample of 121 American workers is drawn from the population. What is the chance that the sample average will fall between $12 per hour and $13.50 per hour?

7. There seems to be a "gender gap" in political party preference in the United States, with women more likely than men to prefer Democratic candidates. A psychologist selects a large random sample of registered voters, both men and women. She asks every voter whether they voted for the Democratic or Republican candidate in the last election. Is this an observational study or an experiment? Why? Suppose she was going to create a scatter diagram (yikes! don't try this at home or anywhere else but it's OK if you are trying to solve this problem) using her two variables. Which variable is the independent variable and which one is the dependent variable?

There are 20,000 restaurants in the County of Los Angeles, 60% of them received a letter grade of "A" during inspections, 30% received either a B or a C grade and 10% failed their inspections.

The University has hired you as a temporary worker. Your job is to schedule the next 10 of the Chancellor's dinners (he eats out all of the time). Unfortunately, you don't know about the rating system and you never eat out because you don't have the money. So you listen to your best friend and pick 10 restaurants at random from an internet database of restaurants in Los Angeles.

The Chancellor will give you +2 points if you choose "A" restaurants, no points if you choose "B" or "C" restaurants, and -10 points if you choose a restaurant with a failing grade.

Credit card companies have been harshly criticized for issuing credit cards to college students who then use the cards and wind up with credit problems even before they are old enough to drink (legally...). 9 undergraduates, selected at random, were asked about their current financial situation. Negative amounts are amounts owed to credit card companies, positive amounts are bank account balances. A zero or larger amount would indicate that the student has no credit card debt problem.

The financial states of the 9 are:

-3500, -500, -3999, -1800, 17000, -200, -2750, -3750, -1000

13. Calculate the mean and median of this list.

14. Credit card companies do admit that some students are poor credit risks and should not have credit cards, but that most students are responsible and do not have debt problems related to credit cards. Using the information from this sample of 9 students, test the credit card companies' claim. State the null and alternative hypotheses, perform a test, use a 5% level of significance as your rule, state the resulting p-value and give us your conclusions.

15. Suppose I were to say to you that one of the undergraduates selected in the sample of 9 is unusual. And suppose I ask you to delete that undergraduate from the list and re-do the test. State the new p-value and give us your conclusions. Go ahead and use a 5% level of significance as your rule if you wish.

16. A poll on women's issues interviewed 1,025 women and 472 men randomly selected from the United States. The poll found that 47% of the women said they do not get enough time for themselves.