In: Statistics and Probability
A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing the number of pounds of force applied to the insulator before it breaks. The following data (stored in Force) are from 30 insulators subjected to this testing:
Force |
1870 |
1728 |
1656 |
1610 |
1634 |
1784 |
1522 |
1696 |
1592 |
1662 |
1866 |
1764 |
1734 |
1662 |
1734 |
1774 |
1550 |
1756 |
1762 |
1866 |
1820 |
1744 |
1788 |
1688 |
1810 |
1752 |
1680 |
1810 |
1652 |
1736 |
Provide steps for both answer
(a) Let denote the mean force required to break the insulator. We have to test the hypothesis:
Vs
The assumptions needed to conduct a t test to test the above hypothesis can be listed as:
- Continuous variable - Independence of Observations - Normally distributed variable - Absence of Outliers
(b) Regarding the assumption about the population distribution, the assumption to be satisfied is that of Normality.
(c) To test the assumption in (b), constructing a histogram, using excel,
We get the output:
The histogram appears to be roughly symmetric.We may conclude that the assumptions of normality is satisfied by the given data.
The test statistic to test the claim is given by:
with critical / rejection region of the test being
where = Sample mean, s = sample standard deviation and n = Sample size
From the sample data,
= 16.35
Substituting the values,
Comparing the test statistic with the critical value for n - 1 = 30 - 1 = 29 df at 0.05 level of significance:
Since, t = 74.84 > 1.699 lies in the rejection / critical region, we may reject H0 at 5% level. We may conclude that there is enough evidence to support the claim that the population mean force required to break the insulator is greater than 1,500 pounds.