STAT 303, 503-504, Spring 1996
Prof. H. Joseph Newton

Homework Assignment 8

Instructions

1. Use Stataquest to do a Two-Way ANOVA for each of the following problems. Your analysis should follow the way we have done it in class. (See the Two-Way ANOVA Example handout).
2. Make sure you include the ANOVA table and Interaction plot for each problem.
3. You will have to enter each data set into Stataquest as they are not on the computer already.
4. Make sure you give your conclusions in terms of the scientific question of interest. For example, in the last data set, don't just say reject or not reject the null hypothesis of no interaction. Rather, say what this means in terms of the data.

Data Sets

1. The data below are amino acid levels of males and females for each of three species of millipedes.

   
                      Species 1       Species 2       Species 3
   ------------------------------------------------------------------------
   
     Male               21.5             14.5            16.0
                        19.6             17.4            20.3
                        20.9             15.0            18.5
                        22.8             17.8            19.3
   
     Female             14.8             12.1            14.4
                        15.6             11.4            14.7
                        13.5             12.7            13.8
                        16.4             14.5            12.0
   
   --------------------------------------------------------------------------
   
   

2. An experiment was conducted to study the effect of length of exposure and temperature of solution upon the absorption of a chemical into a certain material exposed to the solution. The response variable is the amount of chemical absorbed.

   
                      Temperature 1    Temperature 2  Temperature 3
   ------------------------------------------------------------------------
   
     Time 1               35.5             91.2            70.1
                          29.7            100.7            64.1
                          31.5             82.4            70.1
   
     Time 2               52.5             71.0            79.4
                          53.3             77.0            77.7
                          55.0             75.6            75.1
   
     Time 3               85.9             87.0            83.0
                          85.2             86.1            87.0
                          80.2             88.1            78.5
   
   --------------------------------------------------------------------------
   
   

3. An experiment was conducted to assess the effects of temperature and humidity on the resistance of a standard type of resistor. The response variable is the actual resistance.

   
                      Temperature 1    Temperature 2  Temperature 3
   ------------------------------------------------------------------------
   
     Humidity 1           23               26              25
                          24               25              26
                          25               26              26
                          24               26              28
   
     Humidity 2           24               24              27
                          24               25              26
                          25               26              28
                          26               26              28
   
   --------------------------------------------------------------------------
   
   

4. A study of lifetimes of stereo cartridges carried out by staff members of a magazine devoted to high fidelity equipment focused on four different brands of cartridges, each designed to track at two grams. To see whether lifetime was affected by choice of record label, three different labels were randomly selected from the population of all labels, and two lifetime observations (hours of playing time) were obtained for each combination of brand of cartridge and record label.

   
                      Label 1         Label 2         Label 3  
   ------------------------------------------------------------
   
       Brand 1          697             718             640
                        658             688             679
   
       Brand 2          635             700             696
                        684             736             665
   
       Brand 3          670             693             675
                        696             659             703
   
       Brand 4          651             668             715
                        678             709             687
   
   ------------------------------------------------------------