1 A machine that fills milk bottles is supposed to have a me

1. A machine that fills milk bottles is supposed to have a mean amount of milk equal to 32 ounces with a standard deviation of 0.1 ounces. Forty-nine bottles were randomly checked and their mean was found to be 31.98 ounces. With T = -1.4 and , state the null and alternative.

a. Ho m = 32 vs Ha m 32             b.   Ho m = 32 vs Ha m >32

c. Ho m = 32 vs Ha m <32              d. none of these

2. In problem 1, classify the test.

A. two-tailed          B. one tailed left           

C. zero tailed         D. one tailed right

3. In problem 1, what is the correct decision?

A. Reject Ho or     B. Do not Reject Ho         

4. State alpha.

5. What is your conclusion?

Solution

Set Up Hypothesis
Null Hypothesis H0: U=32
Alternate Hypothesis H1: U!=32
Test Statistic
Population Mean(U)=32
Given That X(Mean)=31.98
Standard Deviation(S.D)=0.1
Number (n)=49
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=31.98-32/(0.1/Sqrt(49)
Zo =-1.4
| Zo | =1.4
Critical Value
The Value of |Z | at LOS 0.025% is 2.24
We got |Zo| =1.4 & | Z | =2.24
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -1.4 ) = 0.1615
Hence Value of P0.025 < 0.1615, Here We Do not Reject Ho

[ANSWERS]
1. a. Ho m = 32 vs Ha m 32
2. A. two-tailed
3. B. Do not Reject Ho
4. It is equal to 32