A manufacturing company produces electric insulators. You define the variable of

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 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. The data shown below represent the amount of force required to break a sample of 30 insulators. Complete parts a through c below. 8,5,8,7,11,17,23,29,18,33,16,26,21 ,19,34,26,34,34,45,62,4,6,40,39,16,18,21,22,20,27 . Construct a 90% confidence interval for the population mean force. ____less than or equalsmuless than or equals______ (Round to two decimal places as needed.)

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) isvalid? Explain.

Explanation / Answer

Solution:

a)For finding 95% CI for mean we use MINITAB,

Suppose we entered data in C1 cell and labeled it as X.

Steps in MINITAB:

Stat----àBasic statistics------à1-sample t test------à

Variables:X

Options: Confidence level:95

Ok---àOk

95% CI for mean = (18.00,27.93)

b)Assumptions:

• Data must be from a random sample from large population

• Observations in the sample must be independent of each other

• n small, population distribution must be approximately normal

-n large, population need not be approximately normal

c)Here n =30 which is small. Also data seems random as all observation are different.

Also In this case we always assume that population is normal.

Done

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