2 A random sample of 12 cans of string beans is taken from a

2. A random sample of 12 cans of string beans is taken from a canning plant and the sample mean and the sample standard deviation for the net weight (in ounces) of beans was found to be 15.97 and 0.15 respectively. Test the hypothesis that the average weight is 16 ounces against the alternative that it is less than 16 ounces. Use the 10% level of significance.

Solution

t-test For Single Mean
Set Up Hypothesis
Null Hypothesis H0: U=16
Alternate Hypothesis H1: U<16
Test Statistic
Population Mean(U)=16
Sample X(Mean)=15.97
Standard Deviation(S.D)=0.15
Number (n)=12
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =15.97-16/(0.15/Sqrt(11))
to =-0.693
| to | =0.693
Critical Value
The Value of |t ?| with n-1 = 11 d.f is 1.363
We got |to| =0.693 & | t ? | =1.363
Make Decision
Hence Value of |to | < | t ? | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -0.6928 ) = 0.25139
Hence Value of P0.1 < 0.25139,Here We Do not Reject Ho

We don\'t have enough evidence to support it has less than 16