Reconsider the investigation of the manufacturing process that is producing hypodermic needles. Recall that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm.
a. In the context of this study, explain why it is valid to use the theory-based (t-distribution) approach to find a confidence interval?
b. Use the Theory-Based Inference applet to find and report a 95% confidence interval for the average diameter of needles produced by this manufacturing process.
c. Based on the above 95% confidence interval alone, is there evidence that the average diameter of needles produced by this manufacturing process is different from 1.65 mm? How are you deciding?