Based on the report from the Department of Game and Fish a r

Based on the report from the Department of Game and Fish, a researcher wished to estimate how much trout weigh in Trout Creek. A random sample of 5 trout where captured, weighed, tagged and released; the weights recorded in pounds were 2 lb, 4 lb, 6 lb, 7 lb, and 9 lb yielding a sample mean of 5.6 lbs and a sample standard deviation of 2.7. Use a 10% level of significance to test the claim by the Department of Wildlife Conservation agency that mean weight of trout is 6 lbs. Answer is either: sufficient or insufficient. At the 1% level of significant there is __ __ evidence to reject the null hypothesis. Answer is either: less than, greater than, not equal to or approximately equal to. That is, the mean weight is __ __ 6 lb.

Solution

Set Up Hypothesis
Null, H0: U=6
Alternate, H1: U!=6
Test Statistic
Population Mean(U)=6
Sample X(Mean)=5.6
Standard Deviation(S.D)=2.7
Number (n)=5
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =5.6-6/(2.7/Sqrt(5))
to =-0.331
| to | =0.331
Critical Value
The Value of |t | with n-1 = 4 d.f is 2.132
We got |to| =0.331 & | t | =2.132
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -0.3313 ) = 0.7571
Hence Value of P0.1 < 0.7571,Here We Do not Reject Ho

At the 1% level of significant there is n\'t suffcient evidence to reject the null hypothesis. That is, the mean weight is __ approximately equal to 6 lb.