Question

How much experience do supply-chain transportation managers have in their field? Suppose in an effort to estimate this, 41 supply-chain transportation managers are surveyed and asked how many years of managerial experience they have in transportation. Survey results (in years) are shown below. Use these data to construct a 99% confidence interval to estimate the mean number of years of experience in transportation. Assume that years of experience in transportation is normally distributed in the population.

5	8	10	21	20
25	14	6	19	3
3	9	11	2	3
13	2	4	9	4
5	4	21	7	6
3	28	17	23	2
25	8	13	17	27
7	3	15	4	11
6

Appendix A Statistical Tables

(Round the intermediate values to 3 decimal places. Round your answers to 3 decimal places.)

Answer 1

For the given sample data the mean is calculated as:

Mean = (2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 6 + 6 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 10 + 11 + 11 + 13 + 13 + 14 + 15 + 17 + 17 + 19 + 20 + 21 + 21 + 23 + 25 + 25 + 27 + 28)/41
= 443/41
Mean = 10.8049

and Sample standard deviation as:

Since the population standard deviation is not known hence T-distribution is applicable to calculated the confidence interval as:

μ = ± t(s_M)

where:

= sample mean
t = t statistic determined by confidence level and degree of frredom n-1 , using excel formula for T-distribution.
s_M = standard error = √(s²/n)

= 10.8049
t = 2.7 Computed using excel formula at 0.01 leve of significance and degree of freedom n-1 = 41-1= 40 as =T.INV.2T(0.01,40)
s_M = √(7.8969²/41) = 1.23

μ = ± t(s_M)
μ = 10.8049 ± 2.7*1.23
μ = 10.8049 ± 3.335379

99% CI is [7.470, 14.140].

So, the 99% confidence interval of the mean number of years of experience in transportation is {7.470, 14.140}