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 *H*_{0} if *t*
> .

(Click to select) Reject Do not
reject *H*_{0}. 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 *H*0. 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 )

The mean mass of the puppies at five months is 4.37 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):
4.37
4.55
4.54
4.22
4.57
4.60
4.20
4.48
4.51
4.49
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...

The mean mass of the puppies at five months is 4.39 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):
4.48 4.60 4.49 4.54 4.54 4.55 4.50 4.39 4.30 4.20
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...

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