Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 433 grams. Assume the population standard deviation is known to be 23. Is there sufficient evidence at the 0.05 level that the bags are underfilled?

Answer 1

Hypotheses:

Ho: = 434

Ha: < 434 [Left Tailed Test]

Critical value at 0.05 significance level = -1.645

Decision rule: Reject Ho if z < -1.645

Test statistic

z = (433 - 434)/(23/sqrt(41))

z = -0.28

Since this value is not less than -1.645, it doesn't fall in rejection region and hence, we fail to reject Ho. Therefore,

We do not have sufficient evidence to conclude that the bags are underfilled.