Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is overfilling the bags. A 35 bag sample had a mean of 445 grams. Assume the population standard deviation is known to be 12. Is there sufficient evidence at the 0.05 level that the bags are overfilled? Step 1 of 6: State the null and alternative hypotheses.

Answer 1

Solution:

Given in the question

Null hypothesis H0: mean = 444

Alternate hypothesis Ha: mean>444

No. Of sample = 35

Population standard deviation is known = 12

So we will use Z test as population standard deviation is known and sample size is greater than 30

Z = (445-444)/12/Sqrt(35) = 1/12/Sqrt(35) = 5.916/12 = 0.493

This is right tailed test and from z table we found that

P-value = 0.3121

Here we can see that p-value is greater than alpha value (0.3121>0.05) so we are failed to reject the null hypothesis and we don't have significant evidence to support the claim that the bags are overfilled.