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You work for a biomedical engineering start-up that uses a titanium alloy to manufacture hip joints. The femoral head for the joint needs to be precision machined to fit the corresponding socket in the pelvis with an intended diameter of 45 mm and a standard deviation no greater than 0.5 mm. To test the manufacturing process, the following data have been collected.

x1 x2 x3 x4 x5 x6 x7
44.7753 44.35068 45.21798 45.01032 45.63969 45.13967 44.79558

Required:
a. Perform a Hypothesis Test to determine if there is sufficient evidence to reject the claim that the mean of the manufacturing process is sufficient to a significance level of α = 0.05.
b. Perform a Hypothesis Test to determine if there is sufficient evidence to reject the claim that the standard deviation of the manufacturing process is sufficient to a significance level of α = 0.05.

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