Question

A tire company makes 5000 tires an hour on average with a known standard deviation of 50. A sample is taken last hour and 5100 tires were made. Spell out the null and alternate hypotheses that the mean is different than 5000. Evaluate the hypothesis (Accept or Reject) at the following significance levels: 0.01

Answer 1

Null and alternative hypothesis:

$$H _ {0}: \mu = 5 0 0 0$$ $$H _ {1}: \mu \neq 5 0 0 0$$

Significance level: $\alpha = 0.01$

Test statistics:

$$z = \frac {x - \mu}{\sigma} = \frac {5 1 0 0 - 5 0 0 0}{5 0} = 2$$

Let's find critical value:

$$z _ {c r i t i c a l} = z _ {1 - \frac {\alpha}{2}} = z _ {0. 9 9 5} = 2. 5 7 5 8 3$$

Since $z < z_{\text{critical}}$ we fail to reject Null hypothesis. There is not enough evidence to conclude that $\mu \neq 5000$.