The net weight of a bag of flour is guaranteed to be 5 pound

The net weight of a bag of flour is guaranteed to be 5 pounds with a standard deviation of 0.05 pounds. You are concerned that the actual weight is less. To test for this, you sample 25 bags. You find that the average weight of the 25 bags is 4.7 pounds.

State the appropriate null and alternative hypotheses, as well as the decision of the test when using a significance level equal to 5%

The test is: H0: ?= 5 vs Ha: ?<5; and H0 is rejected.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=5
Alternate Hypothesis H1: U<5
Test Statistic
Population Mean(U)=5
Given That X(Mean)=4.7
Standard Deviation(S.D)=0.05
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=4.7-5/(0.05/Sqrt(25)
Zo =-30
| Zo | =30
Critical Value
The Value of |Z ?| at LOS 0.05% is 1.64
We got |Zo| =30 & | Z ? | =1.64
Make Decision
Hence Value of | Zo | > | Z ?| and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -30 ) = 0
Hence Value of P0.05 > 0,Here We Reject Ho

ANS)
The test is: H0: ?= 5 vs Ha: ?<5; and H0 is rejected