A Study Contains a Plot of the Following Data Pairs

question 53

Essay

A study contains a plot of the following data pairs, where x = pressure of extracted gas (microns) and y = extraction time (min): $$\begin{array} { l l l l l l l l l l l } \hline x & 40 & 130 & 155 & 160 & 260 & 275 & 325 & 370 & 420 & 480 \\\hline y & 2.5 & 3.0 & 3.1 & 3.3 & 3.7 & 4.1 & 4.3 & 4.8 & 5.0 & 5.4 \\\hline\end{array}$$
a. Estimate $\sigma$
and the standard deviation of $\hat { \beta } _ { 1 }$
b. Suppose the investigators had believed prior to the experiment that on average there would be an increase of .006 min. in extraction time associated with an increase of 1 micron in pressure. Use the P-value approach with a significance level of .10 to decide whether the data contradicts this prior belief.