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Regression analysis and Hypothesis testing

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The lapping process, which is used to grind certain silicon wafers to the proper thickness, is acceptable only if 'sigma', the population standard deviation of the thickness of dice cut from the wafers, is at most 0.50 mil. Use the 0.05 level of significance to test the null hypothesis 'sigma' = 0.50 against the alternative hypothesis 'sigma' > 0.50, if the thickness of 15 dice cut from such wafer have a standard deviation of 0.64 mil.

a) What is the equation of the regression line for the pairs (X,Y) shown below? Assume Y on X regression line.
b) What Y is predicted when X=72?
X Y
70 127
66 112
75 146
71 131
67 116
62 97.

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Regression analysis, and testing of standard deviation is provided in the solution.

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