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 9.4 with a calculated sample of variance of 0.64. Select a 99% confidence interval for the true mean of damaged items.

a) [8.682, 10.12]
b) [39.48. -25.66]
c) [11.28, 12.72]
d) L-0.7181.0.7181
e) [8.707, 10.09]
f) None of the above

Answer 1

Option f) None of these

Explanation:

We are given the following data set:

Sample size, n = 12

Sample mean = 9.4

Sample standard deviation = 0.64

Confidence interval:

`\bar{x} \pm t_(critical)(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 11 and at}~\alpha_(0.01) = \pm 3.1058`

`9.4 \pm 3.1058((0.64)/(√(12)) ) = 9.4 \pm 0.574 = (8.826,9.974)`