Question

(25%) 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 30 insulators selected for the experiment and organize and store these data: 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 a. Construct a 95% confidence interval estimate for the population mean force. b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)? c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

Answer 1

a)

Let šo denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, 89.551 ã = 1723.400, s2 = 8019.351724, 8 = 89.551, n = 30, standard error = 16.349670 16.350 V30 The critical value is tcritical = t1-095,29 = +0.025,29 2.045230 2.045 At 95 percent confidence level, The margin of error is: S 89.551 *t 1-0.95 ME= vn * t0.025,29 89.551 * 2.045 = 33.402461 33.402 30 ,29 2 V30 a 95 percent confidence interval of population mean u is S =ī + * t 1-0.95 ,29 2 = 1723.400 + 89.551 * to.025,29 V30 = 1723.400 + 89.551 * 2.045 V30 = 1723.400 = 33.402 = (1689.997539,1756.802461) ~ (1690.00, 1756.80)

b) The population distribution is normal.

c) It is not needed, since sample size is large enough (> = 30), the sampling distribution of sample mean can be approximated by normal distribution, using Central limit theorem.