The production rate of a Company has been normally distributed over a period of time. The mean production rate is 100 pieces per day and standard deviation is 9.Recently the board of management introduced new production methods to improve the production rate.Management wants to test whether the production rate is increased or not.
In order to test the hypothesis, the production rates during 100 production shifts are analyzed. It was found that mean production rate is 104.
Take the level of significance is 0.01

So far i have from two tailed test

level of confidence : 99%
Critical value =0.005

$z = \frac{(104 -100) * 10}{9} = 4.444 $

z value for $H_{0} = 2.575 $
Therefore $H_{0} \ $can be rejected.

Im really new to this lesson and really bad in deciding if it shouldbe one tailed or two tailed. Is it correct and if im wrong can someone point me in the correct direction? Thanks.

  • 1
    $\begingroup$ Whether you should use the two tailed or one tailed, depends on what your alternate hypothesis is, namely if it's $\mu \neq \mu_0$ or $\mu > \mu_0$. I think in this case it could be the latter one, and thus the one tailed version. $\endgroup$ – Matti P. Oct 25 '18 at 7:16

You write

Management wants to test whether the production rate is increased or not.

so $H_1$ is $\mu > \mu_0$.

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