is the value of the standard score based on the data under

____ is the value of the standard score based on the data under the assumption that the null hypothesis is true. *.8.16 (a) Soda Company: A packages company that bottles soda in 12 oz. bottles is interested in monitoring the machines to ensure quality control. Over the years ,it has been determined that the machine has a natural standard deviation of .094 oz. and the distribution of the volumes is normally distributed. A quality control manager takes a random sample of the 40 sodas with a sample mean of 12.3 oz. At the 5% level of significance, test the following hypotheses: a) perform a one tail hypothesis, testing the claim that the true mean is 12 as opposed to the machine overfilling the bottles. Thank you!

Solution

Set Up Hypothesis
Null Hypothesis H0: U=12
Alternate Hypothesis H1: U>12
Test Statistic
Population Mean(U)=12
Given That X(Mean)=12.3
Standard Deviation(S.D)=0.094
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=12.3-12/(0.094/Sqrt(40)
Zo =20.1848
| Zo | =20.1848
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =20.1848 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 20.1848 ) = 0
Hence Value of P0.05 > 0, Here we Reject Ho

true mean is 12 as opposed, we have evidence that machine overfilling the bottles