Question

5. A manufacturing company produces electric insulators. To test the strength of the insulators, you apply a force to an insulator until it breaks. You measure the force by observing how many pounds are required to break the insulator. You collect the force data for a random sample of 30 insulators selected for this experiment. The data is in the Excel file for this assignment in the tab Force. 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 the assumption reference is part (b) is valid for this experiment? Explain your answer.

Answer 1

(A)

First we need to find the mean and SD of data set. Following table shows the calculations:

	X	(X-mean)^2
	1870	21491.56
	1728	21.16
	1656	4542.76
	1610	12859.56
	1634	7992.36
	1784	3672.36
	1522	40561.96
	1696	750.76
	1592	17265.96
	1662	3769.96
	1866	20334.76
	1764	1648.36
	1734	112.36
	1662	3769.96
	1734	112.36
	1774	2560.36
	1550	30067.56
	1756	1062.76
	1762	1489.96
	1866	20334.76
	1820	9331.56
	1744	424.36
	1788	4173.16
	1688	1253.16
	1810	7499.56
	1752	817.96
	1680	1883.56
	1810	7499.56
	1652	5097.96
	1736	158.76
Total	51702	232561.2

Sample size n =30 Sample sum: r=51702 Sample mean: 7-Z* -51702/30 =1723.4 Sample standard deviation: 2(x-7) - Esqrt(232561.2/(30-1)) V n-1 =89.5508

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Since populaiton SD is unknown so t critical value will be used. Level of significance: a =0.05 Critical value: t =2.045 Degree of freedom: df =n-1=29 The requried confidence interval is: I ft 1723.4 + (86.5508*2.045/sqrt(30)) =1723.4 + 32.315 =(1691.09,1755.71) Excel function for critical value: ETINV(0.05,29) Hence, the required confidence interval is (1691.09,1755.71).

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(b)

The population distribution should be normally distributed.

(c)

Since sample size is 30 so we can apply CLT. That is we can assume that population is normally distributed.