A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. You collect the force data for 20 insulators selected for the experiment and organize and store these data (force2).
(a) Compute the sample mean and sample standard deviation.
(b) Assuming that the population standard deviation is known as ? = 95, construct a 95% confidence interval estimate for the population mean force.
(c) Assuming that the population standard deviation is unknown, construct a 95% confidence interval estimate for the population mean force.
(d) Comparing the results in (b) and (c), explain the difference.
| Force |
| 1888 |
| 1777 |
| 1666 |
| 1876 |
| 1634 |
| 1784 |
| 1522 |
| 1696 |
| 1592 |
| 1662 |
| 1866 |
| 1764 |
| 1734 |
| 1662 |
| 1734 |
| 1774 |
| 1550 |
| 1756 |
| 1762 |
| 1866 |
Ans:
a)Sample mean=1728.25
sample standard deviation=105.527
b)z=1.96 for 95% confidence level
95% confidenec interval for mean
=1728.25+/-1.96*(105.527/sqrt(20))
=1728.25+/-41.64
=(1686.61, 1769.89)
c)As,population standard deviation is not known,we will use t distribution.
critical t value=tinv(0.05,19)=2.093
95% confidence interval for mean
=1728.25+/-2.093*(105.527/sqrt(20))
=1728.25+/-49.39
=(1678.86, 1777.64)
c)Confidence interval in part c is wider than in part b.
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