A farmer knows that one week after hatching his chickens hav

A farmer knows that one week after hatching his chickens have an average weight of 62.7 ounces. He has purchased a new feed that he hopes will lead to faster growth.   His latest batch of chickens have the following weights (ounces) after one week.

61.4

62.2

65.7

63.3

64.2

66.0

63.1

63.7

66.6

Does this information indicate that his chickens are gaining weight at a faster rate than before?

a) Use = 0.05

b) Use = 0.01

include H_o and H₁, show the bell curve with appropriate shadings and justify your conclusion with a p value or a critical region explanation.

Solution

t-test For Single Mean
Set Up Hypothesis
Null, it remians same growth H0: U=62.7
Alternate, he hopes will lead to faster growth H1: U>62.7
Test Statistic
Population Mean(U)=62.7
Sample X(Mean)=64.02
Standard Deviation(S.D)=1.7704
Number (n)=9
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =64.02-62.7/(1.7704/Sqrt(8))
to =2.237
| to | =2.237

AT 0.05 LOS
Critical Value
The Value of |t | with n-1 = 8 d.f is 1.86
We got |to| =2.237 & | t | =1.86
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.2368 ) = 0.02785
Hence Value of P0.05 > 0.02785,Here we Reject Ho
he hopes will lead to faster growth

AT 0.01 LOS
Critical Value
The Value of |t | with n-1 = 8 d.f is 2.896
We got |to| =2.237 & | t | =2.896
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 2.2368 ) = 0.02785
Hence Value of P0.01 < 0.02785,Here We Do not Reject Ho

AT 0.01 LOS we calim that it remains same