A manufacturer of potato chips would like to know whether it

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444.0 gram setting. Based on a 40 bag sample where the mean is 443.0 grams, is there sufficient evidence at the 0.02 level that the bags are underfilled? Enter the hypotheses H_o: H_a: Enter the value of the z test statistic. Round your answer to two decimal places. Specify if the test is one-tailed or two-tailed. One-Tailed Test Two-Tailed Test

Solution

Set Up Hypothesis
Null Hypothesis H0: U=444
Alternate Hypothesis H1: U<444
Test Statistic
Population Mean(U)=444
Given That X(Mean)=443
Standard Deviation(S.D)=23
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=443-444/(23/Sqrt(40)
Zo =-0.275
| Zo | =0.275
Critical Value
The Value of |Z | at LOS 0.02% is 2.05
We got |Zo| =0.275 & | Z | =2.05
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Left Tail - Ha : ( P < -0.275 ) = 0.3917
Hence Value of P0.02 < 0.3917, Here We Do not Reject Ho

[ANSWERS]
1. H0: U=444 , H1: U<444
2. Zo =-0.275
3. One Tailed Test
4. Reject Ho if Z<2.05
5. Do not Reject Ho