Two suppliers manufacture a plastic gear used in a laser printer. The impact str

Question

Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in X_1 = 289.30 and s_1 = 22.6, and another random sample of 16 gears from the second supplier results in x_2 = 321.50 and s_2 = 21. Is there sufficient evidence to conclude that the variance of impact strength is different for the two suppliers? Use alpha = 0.05. Round numeric answer to 2 decimal places. Since the test statistic, f_0 =

Explanation / Answer

Answer:

For checking whether there is sufficient evidence to conclude that the variance of impact strength is different for two suppliers. For checking this claim, we have to use F test for population variances.

We have

Level of significance = alpha = 0.05

First sample size = n1 = 10

Second sample size = n2 = 16

Test statistic formula is given as

F = S1^2/S2^2 = 22.6^2/21^2 = 1.1582

Sample 1 degrees of freedom = 10 – 1 = 9

Sample 2 degrees of freedom = 16 – 1 = 15

Critical value F = 3.1227 (By using excel)

P-value = 0.7697 (By using excel)

Required answer: F0 = 3.1227

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