Question

17. A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown below.

	Process A	Process B
Sample mean	2.0	3.0
Standard deviation	1.0	0.5
Sample size	12	14

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, which of the following is the correct decision?

Multiple Choice

• Reject the null hypothesis and conclude the means are different.

• Reject the null hypothesis and conclude the means are the same.

• Fail to reject the null hypothesis.

• Fail to reject the null hypothesis and conclude the means are different.

Answer 1

Given that,

For Process A : n1 = 12, x1-bar = 2.0 and s1 = 1.0

For Process B : n2 = 14, x2-bar = 3.0 and s2 = 0.5

The null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 ≠ μ2

The population standard deviations are unknown but are assumed equal.

Pooled varinace is,

Test statistic is,

=> Test statistic = t = -3.299

Degrees of freedom = 12 + 14 - 2 = 24

t-critical values at significance level of 0.01 with 24 degrees of freedom are, tcrit = ± 2.797

Since, test statistic = -3.299 < -2.797, we reject the null hypothesis.

Answer : Reject the null hypothesis and conclude that the means are different.