Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 414414 gram setting. It is believed that the machine is underfilling the bags. A 1616 bag sample had a mean of 405405 grams with a variance of 625625. A level of significance of 0.0250.025 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

Null hypothesis (Ho) = Mean of the population of machine filling the bag greater than or equal to 414 grams (mu = 414)

Alternate hypothesis (Ha) = Mean of the population of the machine filling the bag is less than 414 grams (mu < 414)

Since it is a lesser than sign in the alternate hypothesis, we need to use a left tailed test.

In the sample we have

Average (x-bar) = 405 grams

Variance (sigma sq.) = 625

Standard deviation (sigma) = 25

Number of samples (n) = 16

Thus we have our test statistics as

Z = ( x-bar – mu ) / (sigma / sqrt(n))

Z = 405 – 414 / (25/4) = -1.44

Now since we have been given a level of significance of 0.025, the z value is -2.81. This is the critical region.

Since the test statistics is not beyond the critical region ( -1.44 > -2.81) we can reject the null hypothesis.

Thus the answer is that we do not have enough evidence to support the claim that bags are under filled.