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. What is the null hypothesis?

Multiple Choice

H0: µA = µB


H0: µA ≠ µB


H0: µA ≤ µB


H0: µA > µB



The null hypothesis (H₀) typically represents a statement of no effect or no difference. In this case, the researcher is interested in determining whether there is evidence that the two processes yield *different* average errors. This suggests a comparison of the means of the two processes.

Given that the question is about testing whether the two processes yield different average errors, the null hypothesis would suggest that there is **no difference** between the two means (i.e., the errors are the same on average for both processes).

The correct null hypothesis is:

**H₀: µA = µB**

This is the option that asserts there is no difference in the average error between Process A and Process B, which the researcher would test against an alternative hypothesis that the means are different.

### Answer: **H₀: µA = µB**

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Would you like further details on hypothesis testing or have any other questions?

Here are 5 related questions to explore:
1. How do you perform a two-sample t-test for comparing two means?
2. What is the alternative hypothesis for this test?
3. What are the assumptions of a t-test for comparing two means?
4. How do you calculate the test statistic for this hypothesis test?
5. How do you interpret the p-value in a hypothesis test?

**Tip:** Always check the assumptions of your statistical test (like equal variances, normality) before conducting the test to ensure its validity.

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. 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. What is the null hypothesis? Process A: sample mean = 2.0, standard deviation = 1.0, sample size = 12. Process B: sample mean = 3.0, standard deviation = 0.5, sample size = 14. Multiple choice: H0: µA = µB, H0: µA ≠ µB, H0: µA ≤ µB, H0: µA > µB.

Determine the null hypothesis for comparing two manufacturing processes in a ball bearings company. The problem uses hypothesis testing, specifically a two-sample t-test, to evaluate the average errors from Process A and Process B. This is a key topic in statistics, involving the comparison of means when population variances are unknown but assumed equal.

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