Statistics Problem Set #1f

Use the following data sets for the calculations in this problem set. These data have a random normal distribution. These are all concentrations (ppb) for replicate samples:

• Set #1; 15.4777, 15.2933, 15.3733, 15.0095, 12.4335, 14.1036, 12.8666, 15.0450, 13.7272, 13.0333, 12.9154, 13.2251, 14.8369, 13.6327, 14.1342, 15.8927, 12.9417, 14.0028, 15.6614, 15.3388, 9.6486, 10.7643, 14.3090, 13.0762, 12.2034
• Set #2; 14.0653, 13.8190, 14.8346, 17.2876, 15.2131
• Set #3; 21.3862, 20.9892, 21.8017, 23.5271, 22.2707
• Set #4; 24.6426, 23.2871, 22.9567

•

1. Descriptive Statistics.
1. Determine the average and standard deviation for each data set.

2.

3. Determine the following confidence intervals (2 sided) for each data set. (Hint, you can find large tables for the tcritical in statistics reference books (There are several good ones in our library, including the CRC handbook of statistics). Also most spreadsheet programs can calculate the tcritical for any confidence interval but you will have to read the help to figure out how to use this function.)

4.

1. 68%
2. 90%
3. 95%
4. 99%
5. 99.9%

6.

2. Comparison Tests.
1. For the Set #1 and Set#2; compare the means, and determine if there is a significant difference between the two means at the 95% Confidence Interval.

2.

3. For Set #3 and Set #4; Compare the means, and determine if there is a significant difference between the two means at the 99% Confidence Interval.

4.

5. For the experiments with Set #3, and Set #4, I am really interested in finding if Set #4 is significantly larger than Set #3. Determine if this is true at the 90% Confidence Interval. (Hint: think about how many sides the distributions could overlap for this test.)

6.

7. Determine if there is a significant difference between the true value and the experimental value (from the data set) at the 95% Confidence Interval. The true values for the data sets are:

8.

1. Set #1 14.0
2. Set #2 14.0
3. Set #3 22.0
4. Set #4 24.0

3. z-Score. For set #1, normalize the data by z-scoring (calculate z for each measurement). What is the average and standard deviation of the z-scored data?

4. Rejection of outliers. For set #2 use the Q-test to determine if 17.2876 is an outlier.