In a Metal Fabrication Process, Metal Rods Are Produced to a Specified

Question

Examlex · Accepted Answer

The Answer is a. Describe the sampling distribution for the sample mean.
The sampling distribution for the sample mean can be modeled using the

t

-distribution with 15 degrees of freedom.
b. What is the standard error?

S E ( \bar { y } ) = \frac { s } { \sqrt { n } } = \frac { 0.65 } { \sqrt { 16 } } = 0.1625 \mathrm { ft }

c. For

95 \%

confidence, what is the margin of error?

t _ { n - 1 } ^ { * } imes S E ( \bar { y } ) = 2.131 imes 0.1625 f t = 0.346 f t

d. Based on the sample results, create the

95 \%

confidence interval and interpret.

\bar { y } \pm t _ { n - 1 } ^ { * } imes S E ( \bar { y } ) = 14.8 \pm 0.346

The

95 \%

confidence interval for true mean length is from

14.454

to

15.146 \mathrm { ft }

. We are

95 \%

confident that the average length of metal rods from this process is between

14.454

and

15.146 \mathrm { ft }

.

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