Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 424.0 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 419.0 grams. A level of significance of 0.05 will be used. Determine the decision rule. Assume the standard deviation is known to be 13.0. Enter the decision rule.

Answer #1

Given that, sample size ( n ) = 39

sample mean = 419.0 grams

population standard deviation = 13.0

Level of significance = 0.05

The null and the alternative hypotheses are,

Since, it is left-tailed test and population standard deviation is known we used z-test.

critical value at 0.05 level of significance is, Z^{*} =
-1.645

Therefore, decision rule is,

Reject the null hypothesis ( H_{0}), if test statistic
is less than -1.645

That is, reject H_{0} , if Z < -1.645

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