Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 448 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 440 grams with a standard deviation of 14. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answer 1

Solution :

Given that,

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 448

Ha: 448

The test statistics,

t = ( - )/ (s/)

= ( 440 - 448 ) / ( 14 / 22 )

= -2.680

P-value = 0.007

The p-value is p = 0.007 < 0.01, it is concluded that the null hypothesis is rejected.

There sufficient evidence to support the claim that the bags are underfilled.