Question

A manufacturing company is purchasing metal pipes of standard length from two different suppliers, ABC and XYZ. In the past two months there are increasing complaints by the Production Manager that delivery times by ABC present higher variability in comparison to the delivery times by XYZ. The Production Manager is worried that this variability will make it harder to efficiently schedule the production process. Does the sample data indicate a statistically significant difference at the 5% level? Justify your answer. Based on your conclusion, which possible error could you be making? Type I or type II error?

Delivery Times(in Hours) by Suppliers ABC and XYZ on Selected Orders
Order	Supplier ABC		Order	Supplier XYZ
1	35		1	19
2	26		2	23
3	26		3	22
4	30		4	21
5	25		5	26
6	20		6	24
7	24		7	23
8	25		8	17
9	19		9	24
10	27		10	21
11	29		11	28
12	25		12	30
13	12		13	20
14	20		14	34
15	22		15	23
16	17		16	26
17	21		17	28
18	16		18	28
19	32		19	26
20	23		20	30
21	29		21	36
22	22		22	22
23	12		23	20
24	28		24	22
25	24		25	21
26	27
27	18

Answer 1

Variance of ABC, s12 = 31.57

Variance of XYZ, s22 = 21.51

Level of significance = 0.05

Degrees of freedom for ABC: df1 = n1-1 = 27-1 = 26

Degrees of freedom for XYZ: df1 = n2-1 = 25-1 = 24

H0: σ12 = σ22, Delivery times by ABC do not present higher variability in comparison to the delivery times by XYZ

H1: σ12 > σ22, Delivery times by ABC present higher variability in comparison to the delivery times by XYZ

Test statistic: F = s12 / s22 = 31.57/21.51 = 1.47

Critical value (Using Excel function F.INV.RT(probability,df1,df2)) = F.INV.RT(0.05,26,24) = 1.97

Since test statistic is less than critical value, we reject the null hypothesis and conclude that σ12 > σ22.

So, delivery times by ABC present higher variability in comparison to the delivery times by XYZ.

Type 2 Error: Accepting an alternate hypothesis that is false