Question

# The mean mass of the puppies at five months is 4.35 kg. The masses follow the...

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 4.3 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.)

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 )

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