Question

A manufacturing company produces electrical insulators. If the insulators break while 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.

1. At the ? = 0.05 level of significance, conduct a formal hypothesis test to determine if there is evidence that the population mean force is greater than 1600 lbs?

2. Construct a 95% confidence interval on population mean force.

3. What assumptions about the population distribution are needed in order for the procedures in parts (1) and (2) above to be valid?

4. Construct the appropriate plot(s) to evaluate the assumptions made in part (3) above. Do you think the

   assumptions are valid? Explain.

DATA:

Observation	Force (lbs)
1	1870
2	1866
3	1820
4	1728
5	1764
6	1744
7	1656
8	1734
9	1788
10	1610
11	1662
12	1688
13	1634
14	1734
15	1810
16	1784
17	1774
18	1752
19	1522
20	1550
21	1680
22	1696
23	1756
24	1810
25	1592
26	1762
27	1652
28	1662
29	1866
30	1736

Answer 1

1. At the ? = 0.05 level of significance, conduct a formal hypothesis test to determine if there is evidence that the population mean force is greater than 1600 lbs?

The hypothesis being tested is:

H₀: µ = 1600

H_a: µ > 1600

1,600.000	hypothesized value
1,723.400	mean Force (lbs)
89.551	std. dev.
16.350	std. error
30	n
29	df
7.548	t
1.28E-08	p-value (one-tailed, upper)

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the population mean force is greater than 1600 lbs.

1. Construct a 95% confidence interval on population mean force.

The 95% confidence interval on population mean force is between 1,689.961 and 1,756.839.

1. What assumptions about the population distribution are needed in order for the procedures in parts (1) and (2) above to be valid?

The data follow the normal probability distribution.

The sample is a simple random sample from its population.

Each individual in the population has an equal probability of being selected in the sample.

1. Construct the appropriate plot(s) to evaluate the assumptions made in part (3) above. Do you think the assumptions are valid? Explain.

Yes, the assumptions are valid.