Hypothesis
t Test for Differences in Two Means
Data
Hypothesized Difference 0
Level of Significance 0.01
Population 1 Sample
Sample Size 12
Sample Mean 0.002
Sample Standard Deviation 0.0001
Population 2 Sample
Sample Size 14
Sample Mean 0.0026
Sample Standard Deviation 0.00012
Intermediate Calculations
Population 1 Sample Degrees of Freedom 11
Population 2 Sample Degrees of Freedom 13
Total Degrees of Freedom 24
Pooled Variance 1.24E-08
Difference in Sample Means -0.0006
t Test Statistic -13.70568
Two-Tail Test
Lower Critical Value -2.796939
Upper Critical Value 2.796939
p -Value 7.61E-13
Reject the null hypothesis
Page 1
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings
Process A Process B
Mean 0.002mm 0.0026mm
Standard Dev 0.0001mm 0.00012mm
Sample Size 12 14
What is the critical t value at the 1% level of significance?
A) +2.779
B) -2.492
C) ±1.711
D) ±2.797
What is the computed value of t?
A) +2.797
B) -2.797
C) -13.7
D) +13.7
What is the decision at the 1% level of significance?
H0: There is no difference between the error levels in the two processes
Ha: There is a significant difference between the error levels in the two processes
Decision: Reject H0 and accept Ha; that is, there is a significant difference between the error levels in the two processes.
producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from ea
ror levels in the two processes.
stry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are
ard is calculated. The results are presented below.