Consider the Following Data on Mass Rate of Burning X

Consider the following data on mass rate of burning x and flame length y: $$\begin{array}{l}\begin{array} { l l l l l l l l } \hline x & 1.7 & 2.2 & 2.3 & 2.6 & 2.7 & 3.0 & 3.2 \\\hline x & 1.3 & 1.8 & 1.6 & 2.0 & 2.1 & 2.2 & 3.0 \\\hline\end{array}\\\\\begin{array} { l l l l l l l } \hline x & 3.3 & 4.1 & 4.3 & 4.6 & 5.7 & 6.1 \\\hline x & 2.6 & 4.1 & 3.7 & 5.0 & 5.8 & 5.3 \\\hline\end{array}\end{array}$$
a. Estimate the parameters of a power function model.
b. Assume that the power function is an appropriate model, test $$H _ { 0 } : \beta = 4 / 3 \text { vs. } H _ { \pm } : \beta < 4 / 3 ,$$
using a level .05 test.
c. 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.