From a population of cans of coffee marked 12 ounces a rando

From a population of cans of coffee marked \"12 ounces\", a random sample of 41 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.80 ounces and a sample standard deviation of 0.5 ounces. At a 1%(0.01) level of significance, test to see if the mean of the population differs from 12 ounces. What is your Conclusion?

Solution

Set Up Hypothesis
Null, H0: U=12
Alternate, mean of the population differs from 12 ouncesH1: U!=12
Test Statistic
Population Mean(U)=12
Sample X(Mean)=11.8
Standard Deviation(S.D)=0.5
Number (n)=41
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =11.8-12/(0.5/Sqrt(41))
to =-2.561
| to | =2.561
Critical Value
The Value of |t | with n-1 = 40 d.f is 2.704
We got |to| =2.561 & | t | =2.704
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -2.5612 ) = 0.0143
Hence Value of P0.01 < 0.0143,Here We Do not Reject Ho

[ANSWER]

We don\'t have evidence to indicate that mean of the population differs from 12 ounces