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2.66 A manufacturing company produces steel housings for elec- trical equipment. The main component part of the housing is a steel trough that is made from a 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weather- proofing in outdoor applications. The widths (in inches), shown in the next column and stored in Trough, are from a sample of 49 troughs: Trough
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math   Statistics-And-Probability   
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The formula for calculating the sample mean is (8.312+8.422 +.+8411) 49 (412.624) -8.420897959 x 8.42089 Therefore, the sample mean is X 842089 The formula for calcualting the stan dard deviation is Σ(8.312-8.4208)+(8.422-8.4208) 49-1 +(8411-84208)2 (0.102075) 48 0.002127 =0 0461 14658 S 0.04611 Therefore, the stan dard deviation is s0.04611 The 95% confidence interval estimate for the mean width of the troughs is The Sample size is n = 49 The Sample Mean is 1-842090 The Sample stan dard deviation s 0.04611 49-1 -48 The level of significance is α-0.05 The table values are caculated by using the excel function = tiny(probability,degrees of freedom -tiy(0.05,48) -2.010634758 2.010634758 The formula for calculating the 95% confidence interval for the population mea 13 ) (m) )su 842090+2010634758(004611) 0.04611 0.04611 8,42090 2.010634758 SHS8.42090+2.010634758 090-2010634758(0 0.04611 8.42090-2010634758| | μ 8.42090 + 2.010634758|-- 8.42090-2010634758(0.006587 143)s μ 842090 + 2.0 10634758 (0.006587143) 8,42090 0.013244338 SS842090+0.013244338 : 8407655662 μ 8 434 144338

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