Question

The mean mass of the puppies at five months is 4.35 kg. The masses follow the normal distribution. In an effort to increase their mass, a supplement is added to their daily meals. The subsequent masses of a sample of five-month-old puppies were (in kilograms):

4.39

4.32

4.28

4.58

4.37

4.48

4.25

4.55

4.30

4.53

a. At the 0.01 level, has the supplement increased the mean mass of the puppies? (Round the final answer to 3 decimal places. Negative answers should be indicated by a minus sign.)

Value of the test statistic

Reject H₀ if t >  .

(Click to select)  Reject  Do not reject  H₀. There is  (Click to select)  enough  not enough  evidence to conclude that the additive increased the mean weight of puppies.

b. Determine or estimate the p-value. (Round the final answer to 4 decimal places.)

  

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 44.05 / 10 = 4.405
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 0.132 / 10 -1 ) = 0.1211

To Test :-

H0 :- µ = 4.35
H1 :- µ > 4.35

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 4.405 - 4.35 ) / ( 0.1211 / √(10) )
t = 1.4362

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.01 , 10-1) = 2.821

t > 2.821

t > t(α, n-1) = 1.4362 < 2.821
Result :- Fail to reject null hypothesis

Do not reject  H0. There is not enough  evidence to conclude that the additive increased the mean weight of puppies.

Part b)

P - value = P ( t > 1.4362 ) = 0.0924 ( From t table )