Question

The existing record shows machine bearing has a mean diameter of 0.6 inches. Bearing diameter is known to be normally distributed with standard deviation σ = 0.1 inches. (Additional note: If the mean diameter of bearings is larger or smaller than 0.6 inches, then the process is out of control and must be adjusted.) A random sample of 60 bearings are selected, and the average diameter of the bearing from this sample is 0.55 inches. Use α=0.02 to test the hypothesis whether the mean diameter of the population bearing is 0.6 inch, and decide whether the process is out of control or not?

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses are as follows :

Test statistic :

To test the hypothesis the most appropriate test is one sample z-test for mean. The test statistic is given as follows :

Where, x̅ = 0.55 inches,  μ = 0.6 inches,  σ = 0.1 inches and n = 60

The value of the test statistic is -3.873.

P-value :

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows :

P-value = 2.P(Z > |z|)

We have, |z| = 3.873

P-value = 2.P(Z > 3.873)

P-value = 0.0001

The p-value is 0.0001.

Decision :

Significance level (α) = 0.02 and p-value = 0.0001

(0.0001 < 0.02)

Since, p-value is less than the significance level of 0.02, therefore we shall reject the null hypothesis (H_{​​​​​​0}) at 0.02 significance level.

Conclusion :

At 0.02 significance level, there is sufficient evidence to conclude that the mean diameter of the population bearing is not 0.6 inch and hence, process is out of control.

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