Question

# A manufacturing company is purchasing metal pipes of standard length from two different suppliers, ABC and...

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

 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.

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