Question

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 insuators, 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.
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 the assumption needed in order to construct the confidence interval estimate in (a) is valid? explain.

Answer 1

Answer:

A)

Note that              

             

Lower Bound = X - z(alpha/2) * s / sqrt(n)              

Upper Bound = X + z(alpha/2) * s / sqrt(n)              

             

where              

alpha/2 = (1 - confidence level)/2 =    0.025          

X = sample mean =    1723.4          

z(alpha/2) = critical z for the confidence interval =    1.959963985          

s = sample standard deviation =    89.55083319          

n = sample size =    30          

             

Thus,              

             

Lower bound =    1691.355235          

Upper bound =    1755.444765          

             

Thus, the confidence interval is              

             

(   1691.355235   ,   1755.444765   ) [ANSWER]

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b)

We assumed taht the distirbution of these observations is approximately normally distributed.

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c)

Yes, because the values are not far away from each other.