The following data on mass rate of burning x and flame length y is representative of that which appeared in the article “Some Burning Characteristics of Filter Paper” (Combustion Science and Technology, 1971: 103–120):

x | 1.7 2.2 2.3 2.6 2.7 3.0 3.2 y | 1.3 1.8 1.6 2.0 2.1 2.2 3.0 x | 3.3 4.1 4.3 4.6 5.7 6.1 y | 2.6 4.1 3.7 5.0 5.8 5.3

a. Estimate the parameters of a power function model.

b. Construct diagnostic plots to check whether a power function is an appropriate model choice.

c. Test H0: 


4 3

 versus Ha:   

4 3

, using a level .05 test.

d. Test the null hypothesis that states that the median flame length when burning rate is 5.0 is twice the median flame length when burning rate is 2.5 against the alternative that this is not the case.