3.3.16 Reconsider the investigation of the manufactur- ing 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 con- fidence 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 pro- duced by this manufacturing process is different from 1.65 mm? How are you deciding?

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3.3.16 Reconsider the investigation of the manufactur-
ing 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 con-
fidence 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 pro-
duced by this manufacturing process is different from
1.65 mm? How are you deciding?
Transcribed Image Text:3.3.16 Reconsider the investigation of the manufactur- ing 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 con- fidence 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 pro- duced by this manufacturing process is different from 1.65 mm? How are you deciding?
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