Question

Provided in the date below a set of restoration times for 35 failed power transformers. The data were collected for recent transformer failures by a fairly novice work crew. a. What is a 90% confidence interval for mean restoration time? b. What is a 99% confidence interval for mean restoration time? c. If the industry standard for such a restoration is 2.7 hours, discuss how well the work crew in this analysis performed.

2.2

1.7

2.4

2.5

2.9

4.4

5.1

1.8

3.2

2.2

1.9

4.4

5.2

5.6

2.5

4.5

3.7

4.3

4.3

2.4

3.6

2.5

1.9

2.7

4.5

3.3

3.9

2.7

3.8

3.9

3.3

2.1

1.6

1.5

2.9

Answer 1

A)
sample mean, xbar = 3.18
sample standard deviation, s = 1.131
sample size, n = 35
degrees of freedom, df = n - 1 = 34

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.691

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3.18 - 1.691 * 1.131/sqrt(35) , 3.18 + 1.691 * 1.131/sqrt(35))
CI = (2.86 , 3.5)

B)
Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.728

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3.18 - 2.728 * 1.131/sqrt(35) , 3.18 + 2.728 * 1.131/sqrt(35))
CI = (2.66 , 3.7)

C)
For 90% CI, the value of 2.7 is below the lower limit of the calculated CI. Hence crew worked below the industry standard.

For 99% CI, the valeu of 2.7 is included in the CI. Hence crew worked as per the industry standard.