include Ho and H1 show the bell curve with appropriate shadi

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. 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

Solution

t-test For Single Mean
Set Up Hypothesis
Null, gaining weight at a lessar or equal rate than before H0: U<=62.7
Alternate, gaining weight at a faster rate than before 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
a)
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

gaining weight at a faster rate than before

b)
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

gaining equal or lessar rate than before