A graphing calculator is recommended. Three students, Linda, Tuan, and Javier, a
ID: 3218159 • Letter: A
Question
A graphing calculator is recommended.
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.)
Enter an exact number as an integer, fraction, or decimal.
df(num) =
Enter an exact number as an integer, fraction, or decimal.
df(denom) =
State the distribution to use for the test.
A. F2, 12
B.F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? (Round your answer to two decimal places.)
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 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.
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 less 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 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.
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 hypothesisdo not reject the null hypothesis
(iii) Reason for decision:
Since < p-value, we do not reject the null hypothesis.
Since > p-value, we reject the null hypothesis.
Since < p-value, we reject the null hypothesis.
Since > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
Weights of Student Lab Rats Linda's rats Tuan's rats Javier's rats 46.3 49.8 53.3 42.3 42.7 43.1 44.1 41.8 40.2 48.7 48.9 47.7 40.8 46.5 51.5Explanation / Answer
Answer:
Enter an exact number as an integer, fraction, or decimal.
df(num) =2
Enter an exact number as an integer, fraction, or decimal.
df(denom) =12
State the distribution to use for the test.
Answer: A. F2, 12
B.F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? 0.52 (Round your answer to two decimal places.)
What is the p-value? 0.6056 (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
A. 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.
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 less 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.
Answer: D. 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.
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.)
= 0.10
(ii) Decision:
not reject the null hypothesis
(iii) Reason for decision:
Answer: Since < p-value, we do not reject the null hypothesis.
Since > p-value, we reject the null hypothesis.
Since < p-value, we reject the null hypothesis.
Since > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
Answer: There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
One factor ANOVA
Mean
n
Std. Dev
44.44
5
3.145
Linda's rats
45.94
5
3.592
Tuan's rats
47.16
5
5.517
Javier's rats
45.85
15
4.066
Total
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
18.561
2
9.2807
0.52
.6056
Error
212.916
12
17.7430
Total
231.477
14
One factor ANOVA
Mean
n
Std. Dev
44.44
5
3.145
Linda's rats
45.94
5
3.592
Tuan's rats
47.16
5
5.517
Javier's rats
45.85
15
4.066
Total
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
18.561
2
9.2807
0.52
.6056
Error
212.916
12
17.7430
Total
231.477
14
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