Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 429.0 gram setting. It is believed that the machine is underfilling the bags. A 40 bag sample had a mean of 425.0 grams. A level of significance of 0.02 will be used. Determine the decision rule. Assume the standard deviation is known to be 11.0.

Enter the decision rule.

Answer 1

Solution:

Given:

We have to test if mean amount of weight is less than 429.0 gram or not.

thus hypothesis are:

Vs  

Level of significance =  

Sample size = n= 40

Population standard deviation is known and we have to determine the decision rule.

Since population standard deviation is known and sample size n is large, we use z distribution ( standard Normal distribution) to find decision rule.

Alternative hypothesis H1 is < type, thus this is two tailed test, hence we look for area 0.0200 in left tail of z table.

Look in z table for area = 0.0200 or its closest area and find corresponding z value.

Area 0.0202 is closest to 0.0200 and it corresponds to -2.0 and 0.05

thus z = -2.05

thus decision rule is:

Reject null hypothesis H0, if