Practice Quiz 9

Time:  20 minutes.  This quiz is open book, open notes.

Suppose you have developed a 95% confidence interval (CI) of the mean of some pollutant concentration based on 26 biweekly measurements in the year 2000 obtained at an air monitoring station.  The interval is (8, 17) (in parts per million by volume).

1.    Indicate which of the following statements are correct and which are incorrect.  Provide reasons for each.

1. There is a 95% probability that the mean measurement in the year 2001 will be between 8 and 17 ppm.
2. There is a 95% probability that the mean measurement in the year 2001 will be greater than 17 ppm.
3. 95% of the measurements obtained in the year 2000 were between 8 and 17 ppm.
4. 5% of the measurement obtained in the year 2000 were between 8 and 17 ppm.
5. 95% of a statistical distribution that best fits the 26 measurements lies between 8 and 17 ppm.
6. If someone else had obtained 26 independent measurements of the same quantity during the same period using the same sampling technique at the same location, then their estimate of the mean (which uses the same formula as yours) is 95% likely also to be between 8 and 17 ppm.
7. You used a procedure to compute an interval that has a 95% chance of covering the true mean.
8. You used a procedure to compute the interval that has a 100% chance of covering the true mean in 95% of all possible situations.
9. There is a 95% probability that the next measurement will be between 8 and 17 ppm.
10. There is a 95% probability that every one of the next 26 measurements will be between 8 and 17 ppm.
11. At least 95% of the next 26 measurements will be between 8 and 17 ppm.
12. No more than 95% of the next 26 measurements will be between 8 and 17 ppm.
13. In thousands of computer simulations of 26 measurements, 95% of them had a mean between 8 and 17 ppm.
14. The value of 8 equals the mean plus t times the standard error of the data, where t is the 2.5 percentage point of Student's t distribution with 25 degrees of freedom, and the value of 17 equals the mean plus t times the standard error, where t is the 97.5 percentage point of Student's t distribution with 25 degrees of freedom.
15. Same as n, but read "standard deviation" in place of "standard error."

2.    List at least two statistical assumptions about the data needed for the preceding CI to be correct.

Extra credit: list as many more assumptions (statistical, scientific, or practical) as you can in question 2.

Scoring: The passing score is 85.

Note:  There will be a smaller number of statements for question #1 on the actual quiz.

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This page was created 18 March 2001 and updated 19 March 2001 to rephrase 1(g).