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. If the variance of XYZ remains unchanged, what should be the variance of ABC in order to reject the null hypothesis at 5% significance level?

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

σ₁: standard deviation of Supplier ABC

σ₂: standard deviation of Supplier XYZ

Ratio: σ₁/σ₂

F method was used. This method is accurate for normal data only.

Descriptive Statistics

Variable	N	StDev	Variance	95% Lower Bound for σ²
Supplier ABC	27	5.618	31.567	21.107
Supplier XYZ	25	4.638	21.507	14.174

Ratio of Variances

Estimated Ratio	95% Lower Bound for Ratio using F
1.46778	0.746

The hypothesis being tested is:

Null hypothesis	H₀: σ₁² / σ₂² = 1
Alternative hypothesis	H₁: σ₁² / σ₂² > 1
Significance level	α = 0.05

Method	Test Statistic	DF1	DF2	P-Value
F	1.47	26	24	0.174

The p-value is 0.174.

Since the p-value (0.174) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a statistically significant difference.