An important problem in industry is shipment damage. A windshield factory ships

Question

An important problem in industry is shipment damage. A windshield factory ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 12. A random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample of variance of 0.49. Select a 99% confidence interval for the true mean of damaged items.

Explanation / Answer

here std error of mean=std deviation/(n)1/2 =(0.49/12)1/2 =0.2021

for (n-1=11) degree of freedom and 99% CI ; critical value of t =3.1058

hence 99% confidence interval for the true mean of damaged items =sample mean -/+ t*std error

=10.6724 to 11.9276

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