include Ho and H1 show the bell curve with appropriate shadi

include H_o and H₁, show the bell curve with appropriate shadings and justify your conclusion with a p value or a critical region explanation. A bottling company wants to ensure that its products are providing the advertised volume. They sampled 12 cans. The weights (in ounces) are given in the table below.

12.09

12.11

11.99

12.03

12.18

12.08

11.93

12.15

12.17

12.08

12.14

12.21

Historically, the population standard deviation is = 0.11. Test at the = 0.02 level that the cans contain more than 12 ounces.

Solution

Set Up Hypothesis
Null, cans contain less than 12 ounces H0: U < 12
Alternate, cans contain more than 12 ounces H1: U > 12
Test Statistic
Population Mean(U)=12
Given That X(Mean)=12.0967
Standard Deviation(S.D)=0.11
Number (n)=12
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=12.0967-12/(0.11/Sqrt(12)
Zo =3.0453
| Zo | =3.0453
Critical Value
The Value of |Z | at LOS 0.02% is 2.05
We got |Zo| =3.0453 & | Z | =2.05
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 3.0453 ) = 0.0012
Hence Value of P0.02 > 0.0012, Here we Reject Ho
Cans contain more than 12 ounces