A herd of 1500 steer was fed a special highprotein grain for

A herd of 1,500 steer was fed a special highprotein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per steer for the month was more than 5 pounds.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=5
Alternate Hypothesis H1: U>5
Test Statistic
Population Mean(U)=5
Sample X(Mean)=6.7
Standard Deviation(S.D)=7.1
Number (n)=29
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =6.7-5/(7.1/Sqrt(28))
to =1.289
| to | =1.289
Critical Value
The Value of |t | with n-1 = 28 d.f is 1.701
We got |to| =1.289 & | t | =1.701
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.2894 ) = 0.1039
Hence Value of P0.05 < 0.1039,Here We Do not Reject Ho

weight gain per steer for the month was not more than 5 pound