Quiz 9 (retest)

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

An agency purports to have developed a symmetric 90% two-sided confidence limit of the mean arsenic concentration in water as measured in 100 wells throughout southern Bangladesh.  These wells were randomly selected from all those used to supply water to southern Bangladesh (the "water supply").  The interval ranges from 210 parts per billion to 430 ppb.

1.    Indicate which of the following statements are correct and which are incorrect.  Provide reasons for each.  Credit is given only for answers accompanied by reasons.

  1. The mean arsenic concentration in the water supply must be between 210 and 430 ppb .
  2. 90% of the water supply contains between 210 and 430 ppb arsenic.
  3. There is a 95% chance that the average arsenic concentration in the water supply is less than 430 ppb and a 95% chance that the average is greater than 210 ppb.
  4. There is a 90% chance that the average arsenic concentration in the water supply is less than 430 ppb and a 90% chance that the average is greater than 210 ppb.
  5. There is an 80% chance that the average arsenic concentration in the water supply is less than 430 ppb and an 80% chance that the average is greater than 210 ppb.
  6. If another agency attempts to replicate these results by randomly selecting and measuring 100 wells for arsenic, there is a 90% chance its mean will be between 210 and 430 ppb.
  7. If another agency attempts to replicate these results by randomly selecting and measuring 100 wells for arsenic, there is a 90% chance its confidence interval will cover the true mean.
  8. If another agency attempts to replicate these results by randomly selecting and measuring 100 wells for arsenic, there is a 90% chance its confidence interval will overlap with the 210 to 430 ppb range.

2.    To develop the confidence interval in problem 1, the agency assumed the sampling distribution of the mean would be Normal, but of unknown mean and standard deviation.  Estimate the 80% upper confidence limit (UCL) of the mean by using the Normal distribution instead of the (more accurate) Student t distribution.

Scoring: The passing score is 88.

Return to the Environmental Statistics home page

This page is copyright (c) 2001 Quantitative Decisions.  Please cite it as

This page was created 24 March 2001.