Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 445445 gram setting. It is believed that the machine is underfilling the bags. A 1313 bag sample had a mean of 444444 grams with a standard deviation of 1212. A level of significance of 0.010.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

To Test :-
H0 :- µ = 445
H1 :- µ ≠ 445

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 444 - 445 ) / ( 12 / √(13) )
t = -0.3005

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.01 /2, 13-1) = 3.055
| t | > t(α/2, n-1) = 0.3005 < 3.055
Result :- Fail to reject null hypothesis

Decision rule

Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.01 /2, 13-1) = 3.055

Reject null hypothesis if | t | > 3.055