Question

In: Statistics and Probability

A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit...

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:

  1. At the 0.05 level of significance, is there evidence that the population mean force required to break the insulator is greater than 1,500 pounds? Be sure to write out the hypotheses clearly in your output and to clearly state your conclusion.
  2. What assumption about the population distribution is needed in order to conduct the t test in (a)?
  3. Construct a histogram, boxplot, or normal probability plot to evaluate the assumption made in (b). Based on the evidence obtained from the plot, is the assumption needed for the t-test valid? Explain.
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

Solutions

Expert Solution

(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.


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