Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)

Weights of Student Lab Rats

Linda's rats Tuan's rats Javier's rats

43.0 46.9 51.1

38.5 40.1 40.4

40.7 38.4 37.1

45.8 45.7 44.8

37.8 43.6 47.7

Part (a)

State the null hypothesis.

H₀: ?₁ = ?₂ = ?₃

H₀: At least two of the group means ?₁, ?₂, ?₃ are not equal.


Part (b)

State the alternative hypothesis.

H_a: ?₁ = ?₂ = ?₃

H_a: At least two of the group means ?₁, ?₂, ?₃ are not equal.


Part (c)

Enter an exact number as an integer, fraction, or decimal.
df(num) =

Part (d)

Enter an exact number as an integer, fraction, or decimal.
df(denom) =

Part (e)

State the distribution to use for the test.

a. F_{14, 2}

b. F_{2, 12}
c.F_{2, 14}
d. F_{12, 2}

e. F_{14, 12}

Part (f)

What is the test statistic? (Round your answer to two decimal places.)

=

Part (g)

What is the p-value? (Round your answer to four decimal places.)

=

Explain what the p-value means for this problem.
a.If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

b. If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

c.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

D. If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

Part (h)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

Part (i)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? > p-value, we reject the null hypothesis.

Since ? > p-value, we do not reject the null hypothesis.

  Since ? < p-value, we do not reject the null hypothesis.

Since ? < p-value, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection that there is no difference among the different nutritional formulas for rats with respect to weight gain.

There is not sufficient evidence to warrant a rejection that there is a difference among the different nutritional formulas for rats with respect to weight gain.

Question

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)

Weights of Student Lab Rats
Linda's rats	Tuan's rats	Javier's rats
43.0	46.9	51.1
38.5	40.1	40.4
40.7	38.4	37.1
45.8	45.7	44.8
37.8	43.6	47.7

Part (a)

State the null hypothesis.

H₀: ?₁ = ?₂ = ?₃

H₀: At least two of the group means ?₁, ?₂, ?₃ are not equal.
Part (b)

State the alternative hypothesis.

H_a: ?₁ = ?₂ = ?₃

H_a: At least two of the group means ?₁, ?₂, ?₃ are not equal.
Part (c)

Enter an exact number as an integer, fraction, or decimal.
df(num) =
Part (d)

Enter an exact number as an integer, fraction, or decimal.
df(denom) =
Part (e)

State the distribution to use for the test.

a. F_{14, 2}

b. F_{2, 12}
c.F_{2, 14}
d. F_{12, 2}

e. F_{14, 12}
Part (f)

What is the test statistic? (Round your answer to two decimal places.)

=
Part (g)

What is the p-value? (Round your answer to four decimal places.)

=

Explain what the p-value means for this problem.
a.If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

b. If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

c.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

D. If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
Part (h)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.
Part (i)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? > p-value, we reject the null hypothesis.

Since ? > p-value, we do not reject the null hypothesis.

  Since ? < p-value, we do not reject the null hypothesis.

Since ? < p-value, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection that there is no difference among the different nutritional formulas for rats with respect to weight gain.

There is not sufficient evidence to warrant a rejection that there is a difference among the different nutritional formulas for rats with respect to weight gain.

Accepted Answer

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