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Engine parts Here are measurements (in millimeters) of a critical dimension on an SRS of $16$of the more than $200$auto engine crankshafts produced in one day:

$224.120$, $224.001$, $224.017$,$223.982,$$223.989,$$223.960,$$224.089,$$223.987,$$223.976,$$223.902,$$223.980,$$224.098,$$224.057,$$223.913,$$223.999$

(a) Construct and interpret a $95\%$confidence interval for the process mean at the time these crankshafts were produced.

(b) The process mean is supposed to be $渭=224$but can drift away from this target during production. Does your interval from part (a) suggest that the process mean has drifted? Explain.

- Determine the sample size required to obtain a level $C$confidence interval for a population mean with a specified margin of error.

Step by step solution

01

Part (a) Step 1: Given Information

Given in the question that,

$224.120$
$224.001$
$224.017$
$223.982$
$223.989$
$223.961$
$223.960$
$224.089$
$223.987$
$223.976$
$223.902$
$223.980$
$224.098$
$224.057$
$223.913$
$223.999$

we have to construct and interpret a $95\%$confidence interval for the process mean at the time these crankshafts were produced.

02

Part (a) Step 2:  Explanation 

The formula to compute the confidence interval is:

$\overline{x}-t\frac{伪}{2}脳\frac{s}{\sqrt{n}}<渭<\stackrel{炉}{x}+t\frac{伪}{2}脳\frac{s}{\sqrt{n}}$

The confidence interval using Ti-83calculator could be computed as:

Thus there is$95\%$probability that the population mean is between$223.97and227.03$

03

Part (b) Step 1: Given Information 

The process mean is supposed to be $渭=224$ but can drift away from this target during production .we have to find that Does interval from part (a) suggest that the process mean has drifted .

04

Part (b) Step 2:  Explanation 

From the above part, it is known that the population mean process is between $223.97and224.03$Since, the interval is containing $224$ it could be said that the process mean has drifted.

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