Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 404.0 gram setting. It is believed that the machine is underfilling the bags. A 47 bag sample had a mean of 403.0 grams. A level of significance of 0.1 will be used. Determine the decision rule. Assume the variance is known to be 729.00

Enter the decision rule.

QUESTION: Reject H0 if z<

Answer 1

Here we have to test following hypothesis,

$H_0 : \mu = 404$

$H_a : \mu < 404$   { It is believed that the machine is underfilling the bags }

Left tail test.

We have to use z test because population variance $\sigma^2$ is known.

Decision rule :

This is left tail test, so reject null hypothesis H₀ if test statistic $z < -z_{\alpha }$

Where, $-z_{\alpha }$ is left tail z critical value at given significance level $\alpha$

We are given Significance level $\alpha$ = 0.1

So critical value for this left tail test is ,

$-z_{\alpha }$ = $-z_{0.1}$ = -1.2816          { Using Excel function , =NORMSINV( 0.1 ) = -1.2816 }

So, Reject H₀ if z < -1.2816