A machine that is programmed to package 1.20 pounds of cereal is being tested fo

Question

A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. Use Table 2.

Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes.

A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. Use Table 2.

Explanation / Answer

Set Up Hypothesis
Null, H0: U<=1.2
Alternate, machine is overfilling the cereal boxes H1: U>1.2
Test Statistic
Population Mean(U)=1.2
Sample X(Mean)=1.22
Standard Deviation(S.D)=0.06
Number (n)=36
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1.22-1.2/(0.06/Sqrt(36))
to =2
| to | =2
Critical Value
The Value of |t | with n-1 = 35 d.f is 1.69
We got |to| =2 & | t | =1.69
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2 ) = 0.02665
Hence Value of P0.05 > 0.02665,Here we Reject Ho

[ANSWER]
1. H0: µ 1.20; HA: µ > 1.20
2. to =2
3.    0.01 < p-value < 0.025
4.    Reject H0 since the p-value is smaller than .
5. +1.69
6. Yes

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