Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 401 gram setting. Based on a 18 bag sample where the mean is 392 grams and the standard deviation is 19, is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.

Step 1 of 5: State the null and alternative hypotheses.

Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

a)

H0: = 401

Ha: 401

2)

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 392 - 401 ) / ( 19 / √(18) )
t = -2.010
3)

This test is two tailed.

4)  

Decision rule :-

Critical value t(α/2, n-1) = t(0.05 /2, 18-1) = 2.11
Reject null hypothesis if | t | > 2.11

5)

| t | > t(α/2, n-1) = 2.0097 < 2.11
Result :- Fail to reject null hypothesis