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# Critical Value and Decision

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In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 15 students were randomly assignment to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attentions spans (in minutes) were recorded during a morning reading period and are shown below. Is there a significant difference in attention span based on the three meal plans? Identify the appropriate test and use the 0.05 significance level in determining your answer. Assume the populations are normal with equal standard deviations.

No Breakfast Light Breakfast Full Breakfast
8 14 10
7 16 12
9 12 16
13 17 15
10 11 12

Sum X 47 70 65
Sum X^2 463 1006 869
Means: 9.4 14 13
Variances: 5.3 6.5 6

1. Identify the claim
2. Critical Value(s)
3. Test Value

Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses. The hydrocarbons emitted by the potato plant were measured and compared to the plant weight. Weight (x) was measured in grams and hydrocarbon emissions (y) were measured in hundreds of nanograms for 11 plants. Let alpha = 0.05 and use the traditional method to test for a relationship between plant weight and hydrocarbon emissions. Write the hypotheses in sentence form, not with symbols.

X 57 85 57 65 52 67 62 80 77 53 68
Y 8.0 22.0 10.5 22.5 12.0 11.5 7.5 13.0 16.5 21.0 12.0

1. Critical Value(s)
2. Decision

https://brainmass.com/statistics/hypothesis-testing/critical-value-decision-18720

#### Solution Preview

In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 15 students were randomly assignment to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attentions spans (in minutes) were recorded during a morning reading period and are shown below. Is there a significant difference in attention span based on the three meal plans? Identify the appropriate test and use the 0.05 significance level in determining your answer. Assume the populations are normal with equal standard deviations.

No Breakfast Light Breakfast Full Breakfast
8 14 10
7 16 12
9 12 16
13 17 15
10 11 12

Sum X 47 70 65
Sum X^2 463 1006 869
Means: 9.4 14 13
Variances: 5.3 6.5 6

1. Identify the claim
Solution. Assume that their mean attentions spans are , respectively. Then we can set up the null hypothesis as follows.
:
2. Critical Value(s)
3. Test Value ...

#### Solution Summary

In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 15 students were randomly assignment to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attentions spans (in minutes) were recorded during a morning reading period and are shown below. Is there a significant difference in attention span based on the three meal plans? Identify the appropriate test and use the 0.05 significance level in determining your answer. Assume the populations are normal with equal standard deviations.

No Breakfast Light Breakfast Full Breakfast
8 14 10
7 16 12
9 12 16
13 17 15
10 11 12

Sum X 47 70 65
Sum X^2 463 1006 869
Means: 9.4 14 13
Variances: 5.3 6.5 6

1. Identify the claim
2. Critical Value(s)
3. Test Value

Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses. The hydrocarbons emitted by the potato plant were measured and compared to the plant weight. Weight (x) was measured in grams and hydrocarbon emissions (y) were measured in hundreds of nanograms for 11 plants. Let alpha = 0.05 and use the traditional method to test for a relationship between plant weight and hydrocarbon emissions. Write the hypotheses in sentence form, not with symbols.

X 57 85 57 65 52 67 62 80 77 53 68
Y 8.0 22.0 10.5 22.5 12.0 11.5 7.5 13.0 16.5 21.0 12.0