4) 96% Tue 7:56 PM Galo Bu Help Save&ExitSu; A national manufacturer of ball bea

Question

4) 96% Tue 7:56 PM Galo Bu Help Save&ExitSu; A national manufacturer of ball bearings is experimenting with two different processes for producing prec 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 presented here. ProcesS A Process B Sample mean Standard deviation Sample size 2.0 1.0 12 3.0 0.5 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, what is the decision? the null hypothesis and conclude the means are different

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)

Hypothesis test results:

Since p - value is less than 0.01, we reject Ho and conclude that the means are different. Hence,

Option A is correct.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -1 0.31810451 15.612769 -3.143621 0.0064

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