Question

1. Crop yields per acre depend on many variables, but two obvious ones are fertilizer and weed control. In an effort to test the effects of various levels of fertilizer and of herbicide, researchers selected six plots of land and subdivided each into eight pieces. Each of the eight pieces of each plot was treated with one of the eight combinations of fertilizer (none, light, moderate, heavy) and herbicide (none, some). The per acre yields of each piece of land are recorded below:

In the data, levels of fertilizer are 1 (none), 2 (light), 3 (moderate), 4 (heavy) and levels of herbicide are 1 (none) and 2(some).

fert     herb   yield

1        1        64.40

1        1        61.20

1        1        58.34

1        1        59.72

1        1        62.84

1        1        62.59

2        1        59.09

2        1        62.59

2        1        63.71

2        1        64.01

2        1        66.50

2        1        60.11

3        1        64.40

3        1        66.98

3        1        63.78

3        1        66.52

3        1        65.17

3        1        62.33

4        1        54.69

4        1        64.27

4        1        64.40

4        1        63.56

4        1        65.77

4        1        66.07

1        2        57.50

1        2        59.38

1        2        61.04

1        2        61.54

1        2        61.06

1        2        61.64

2        2        66.67

2        2        63.62

2        2        66.20

2        2        65.59

2        2        62.85

2        2        66.07

3        2        70.37

3        2        62.72

3        2        67.85

3        2        63.74

3        2        64.88

3        2        63.96

4        2        61.83

4        2        64.20

4        2        65.94

4        2        67.56

4        2        60.28

4        2        67.75

Give a statement to be tested, identify the random variables involved and the assumptions you make about them, state the hypotheses to be tested, ask SPSS to run the analysis for you, including a post hoc, and then discuss the outcome. Describe the critical region(s) upon which you base your decisions. Include any SPSS output in your discussion.

Answer 1