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? In plain English, please interpret it's meaning.

2. What is the regression equation for predicting time to the next eruption from the duration of an eruption? Please interpret the meaning of the slope and of the intercept terms.

3. You just missed an eruption. The sign at the geyser says "Next Eruption in 50 minutes." Can you tell what the duration of the previous eruption was in minutes? Answer yes or no and 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. Can you predict how long must you wait around to see the next eruption? If yes, please indicate how many minutes it will take. If no, please indicate why this is not possible.

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

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

2. 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?

 

 

 

 

 

 

3. Suppose the sample average of the 121 workers is actually $13.25 with a standard deviation of $6.88. Please test the hypothesis that salaries are increasing over time. State a null hypothesis, an alternative, perform a test, state a p-value and use a 1% level of significance to make a decision. Please state your conclusion in plain English.

6. 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 using her two variables. Which variable is the independent variable and which one is the dependent variable? Would it be possible to calculate a meaningful correlation for these two variables? Explain why or why not.

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. Assume the financial situation of undergraduates is normally distributed.

The financial states of the 9 are:

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

7. Calculate the mean and median of this list.

8. 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.

9. 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.

1. Your friend is taking Statistics10 next quarter (don't worry, I'm not teaching it again this academic year...). Explain the meaning of this confidence interval to your friend.

Your company advertises that it ships 90% of its orders on time, that is, within 5 working days. The average shipping time of all orders is 3.1 days with a standard deviation of 0.4 days. You select a simple random sample (SRS) of 21 of the 10,000 orders received in the past week for an audit. The audit reveals that 18 of the 21 orders were shipped within 5 working days.

10. What is the sample percentage of orders shipped on time and what is the standard error for the percentage of orders shipped on time?

11. A lawyer approaches you and says "Aha! You claim 90% but even in your very own sample the percentage is lower than that. So your 90% claim is wrong." Does the lawyer have enough evidence to sue you for false advertising? Perform a test and use a 5% level of significance as your rule. Explain why the results of your test refute or do not refute your 90% claim.

12. Please answer these questions regarding the confidence interval:

(a) What happens to the width of a confidence interval as the level of confidence increases?

(b) Why would someone choose a 90% level of confidence instead of a 99% level if the 99% level has a greater chance of capturing the population parameter?

(c) If you were told that a researcher was "95% sure that the population mean was within the interval from 84.1 ± 5.3, could you tell me the size of the standard error?

(d) Given the choice of a sample of size 36 or a sample of size 49, which one would you prefer to use to estimate the value of an unknown parameter? Justify your choice in the context of a discussion of the confidence interval.