The Quality Engineer at a Paint Manufacturer Conducted a Hypothesis $\mathrm { H } _ { 0 } : \mu = 1.02$

Essay

The quality engineer at a paint manufacturer conducted a hypothesis test to test the claimthat the mean volume of paint cans had changed after an adjustment in the manufacturingprocess. Mean volume in paint cans before the adjustment was 1.02 gallons. Assume thatall conditions for testing have been met. She used technology to complete the hypothesistest. Following is the null and alternative hypothesis and the output from her graphingcalculator. $\mathrm { H } _ { 0 } : \mu = 1.02$ gallons $\mathrm { H } _ { \mathrm { a } } : \mu \neq 1.02$ gallons $\begin{array} { | l | } \hline \text { T-Test } \\\mu \neq 1.02 \\t = - 5.89255651 \\p = 3.4248373 E - 7 \\\bar { x } = .97 \\S x = .06 \\n = 50 \\\hline\end{array}$ Write a statement explaining what her decision regarding the null hypothesis should beand a statement summarizing her conclusion regarding the claim that average volume ofpaint cans had changed. Has the adjustment in the manufacturing process changed theaverage volume of paint cans?