Question

A manufacturing process ball bearings with diameters that have a normal distribution with known population standard deviation of .03 centimeters. Ball bearings with diameters that are too small or too large are undesirable. In order to test the claim that μ = 0.50 centimeters, perform a two-tailed hypotheses test at the 5% level of significance. A random sample of 49 gave a mean of 0.48 centimeters. Perform a hypotheses test and state your decision.

Answer 1

Let X be the diameter of manufacturing process ball bearings

X~ N(0.50 ,0.03)

Here we want to test

$H_0: \mu = 0.5$

vs

$H_0: \mu \neq 0.5$

Here

$\mu = 0.5 \\ \sigma = 0.03 \\ n =49 \\ \bar x = 0.48$

The test statistic is

$Z = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt n}} = \frac{0.48- 0.5}{\frac{0.03}{\sqrt {49}}} = -0.02\times\frac{7}{0.03} = -4.67$

For the two-tailed test at 5% level of significance the critical value = 1.96

Now |-4.67| > 1.96

So the absolute value of test statistic is greater than the critical value.

Hence we reject H0 at 5% level of significance and conclude that $\mu = 0.5$

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