Reginald Brown an inspector from the Department of Weights a

Reginald Brown, an inspector from the Department of Weights and Measures, weighs 15 eighteen-ounce cereal boxes of corn flakes. He finds their mean weight to be 17.78 ounces with a standard deviation of 0.4 ounces. Are the cereal boxes lighter than they should be? Let alpha = 0.01.

Solution

Set Up Hypothesis
Null, H0: U=18
Alternate, H1: U<18
Test Statistic
Population Mean(U)=18
Sample X(Mean)=17.78
Standard Deviation(S.D)=0.4
Number (n)=15
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =17.78-18/(0.4/Sqrt(15))
to =-2.13
| to | =2.13
Critical Value
The Value of |t | with n-1 = 14 d.f is 2.624
We got |to| =2.13 & | t | =2.624
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -2.1301 ) = 0.02569
Hence Value of P0.01 < 0.02569,Here We Do not Reject Ho

We don\'t have evidence that is lighter than 18