Question-21

T-test and Confidence Interval

The distribution of the diameter of screws produced by a certain machine is normally distributed with \(\mu\) and \(\sigma\) unknown. We observe a random sample \(9.8, 10.2, 10.4, 9.8, 10.0, 10.2\) and \(9.6\) (in cm). Find a 95% confidence interval for the mean diameter of screws.

\([10.74, 11.26]\)
\([9.74, 10.26]\)
\([7.47, 8.26]\)
\([7.98, 8.75]\)

Hint

Use \(P(-0.26<t_6<0.26)=0.95\) and \(s\text{(sample standard deviation)}=0.283\).

Answer

\([10.74, 11.26]\)
\([9.74, 10.26]\)
\([7.47, 8.26]\)
\([7.98, 8.75]\)

Solution