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

Answer:

Option f) None of these

Step-by-step explanation:

We are given the following data set:

Sample size, n = 12

Sample mean  = 9.4

Sample standard deviation = 0.64

Confidence interval:

$\bar{x} \pm t_{critical}\frac{s}{\sqrt{n}}$

Putting the values, we get,

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

$9.4 \pm 3.1058(\frac{0.64}{\sqrt{12}} ) = 9.4 \pm 0.574 = (8.826,9.974)$