problem 1: To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and observe the insects trapped on the boards. Which colors attract insects best? Experimenters placed six boards of each of four colors at random locations in a field of oats and measured the number of cereal leaf beetles trapped. Here is the data:
Use a significance level of 10%:
a) Use all the steps of an appropriate statistical method to find out whether there are differences in the means of the number of cereal leaf beetles, in terms of color preference, mainly based on the numbers trapped on the different colored boards.
b) If suitable, carry out post-hoc multiple comparisons of group means. Describe your results. If you choose to not conduct post-hoc tests, describe why.
c) State any suppositions you have made and assess whether these are met with this data.
problem 2: We think of DNA as the stuff which stores the genetic code. This turns out that DNA takes place mainly outside living cells, on the ocean floor. It is significant in nourishing seafloor life. Scientists think that this DNA comes from organic matter which settles to the bottom from the top layers of the ocean. Phytopigments that come mainly from algae are a measure of the amount of organic matter which has settled to the bottom. The file “dna_oceanfloor.jmp” contains data on concentrations of DNA and phytopigments (that is, both in grams per square meter) in 116 ocean locations around the world. Does the data give good reason to think that Phytopigments concentration helps to elucidate DNA concentration?
a) Using a suitable graphical display, describe the relationship between DNA and phytopigments.
b) Fit a regression line to the data. prepare down the equation of model and interpret all the parameters in the model.
c) Test the hypothesis of no linear relationship among DNA and phytopigments. Illustrate all the steps.
d) Using JMP, obtain 95% confidence intervals for intercept and slope. Interpret.
e) Critically assess the model. Does your assessment propose any problems with the fitted regression model?
f) Predict the DNA concentrations when Phytopigments concentration equals to 0.07 gr/m^{2} and 0.09 gr/m^{2} correspondingly.