For Data Set 1, Body Length Data 1, the calculations have already been provided for you.
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3.For Data Set

1, Body Length Data 1, the calculations have already been provided for you. Which of the following statements correctly summarizes the statistics for the Body Length Data 1 calculations?


a. The F-value was found to be 23.27. Because this is a relatively high F-value, this suggests that there is much more variation across the groups than within the groups. Because there is a higher variation across the groups compared to within the groups, there is a greater chance of this resulting in a significant difference.


b. The F-value was found to be 23.27. Because this is a relatively low F-value, this suggests that there is much less variation across the groups than within the groups. Because there is a lower variation across the groups compared to within the groups, there is a greater chance of this resulting in a significant difference.


c. The F-value was found to be 23.27. Because this is a relatively high F-value, this suggests that there is much more variation across the groups than within the groups. Because there is a higher variation across the groups compared to within the groups, there is a lower chance of this resulting in a significant difference.


d. The F-value was found to be 23.27. Because this is a relatively low F-value, this suggests that there is much less variation across the groups than within the groups. Because there is a lower variation across the groups compared to within the groups, there is a lower chance of this resulting in a significant difference.


e. There is not enough statistical information provided in the calculations to interpret the F-value.




4 .For Data Set 1, Body Length Data 1, the calculations have already been provided for you. Which of the following statements correctly explains the relationship between the F-value, the p-value, and the null hypothesis?


a. The F-value is likely higher than the critical F-value. This resulted in a low p-value. This low p-value means that there is not a significant difference between the populations in body length. Therefore, the null hypothesis should be accepted.


b. The F-value is likely lower than the critical F-value. This resulted in a low p-value. This low p-value means that there is not a significant difference between the populations in body length. Therefore, the null hypothesis should be accepted.


c. The F-value is likely lower than the critical F-value. This resulted in a low p-value. This low p-value means that there is a significant difference between the populations in body length. Therefore, the null hypothesis should be rejected.


d. The F-value is likely higher than the critical F-value. This resulted in a low p-value. This low p-value means that there is a significant difference between the populations in body length. Therefore, the null hypothesis should be rejected.


e. The F-value is likely higher than the critical F-value. This resulted in a low p-value. This low p-value means that there is a significant difference between the populations in body length. Therefore, the null hypothesis should be accepted.

 



5.For Beak Height Data 1, what is the correct F-value, and what does this mean regarding your null hypothesis?


a. F=11.7. This F-value is likely higher than the critical F-value. Therefore, the p-value is <0.05 and the null hypothesis should be rejected.


b. F = 0.117. This F-value is likely lower than the critical F-value. Therefore, the p-value is >0.05 and the null hypothesis should be accepted (or rather, fail to be rejected).


c. F=0.234. This F-value is likely lower than the critical F-value. Therefore, the p-value is >0.05 and the null hypothesis should be accepted (or rather, fail to be rejected).


d. F=23.4. This F-value is likely higher than the critical F-value. Therefore, the p-value is <0.05 and the null hypothesis should be rejected.


e. F=0.458. This F-value is likely higher than the critical F-value. Therefore, the p-value is <0.05 and the null hypothesis should be rejected.




6.After completing the entire set of calculations for Beak Length Data II, what is the correct F value? Choose the answer with the correct SSR mean and SSE mean values used to find the correct F value.


a. 0.77/19.4 = 0.0397


b. 9.7/0.36 = 26.94


c. 11.088/0.44 = 25.2


d. 19.4/0.77 = 25.2


e. 11.8536/0.44=26.94



7.After finding the correct F-value for Beak Length Data II, which statement below correctly explains the relationship between the F-value, the numerator df, the denominator df, the critical F-value, and the p-value?


a. The df numerator is 2 and the df denominator is 12. Therefore, the critical F-value is 3.89. Because the calculated F-value from #4 is lower than this, the p-value will be above 0.05.


b. The df numerator is 3 and the df denominator is 12. Therefore, the critical F-value is 3.49. Because the calculated F-value from #4 is higher than this, the p-value will be below 0.05.


c. The df numerator is 3 and the df denominator is 12. Therefore, the critical F-value is 3.49. Because the calculated F-value from #4 is lower than this, the p-value will be above 0.05.


d. The df numerator is 4 and the df denominator is 12. Therefore, the critical F-value is 3.25. Because the calculated F-value from #4 is higher than this, the p-value will be below 0.05.


e. The df numerator is 2 and the df denominator is 12. Therefore, the critical F-value is 3.89. Because the calculated F-value from #4 is higher than this, the p-value will be below 0.05.

 



8.After completing the entire set of calculations for Beak Height Data II, what is the correct F value? Choose the answer with the correct SSR mean and SSE mean values used to find the correct F value.


a. 0.47/40.2 = 0.012


b. 30.2/1.47 = 20.544


c. 1.47/30.2 = 0.048


d. 40.2/0.47 = 85.5


e. .402/.147 = 2.735



9.What is the most accurate conclusion based on the ANOVA results alone for Beak Height Data II?


a. Two out of the three islands have significant differences in beak heights.


b. There is significant variation in beak heights across the three islands.


c. There is no significant difference in beak height across the three islands.



10.In an ANOVA, what is the general relationship between your calculated F-value and your p-value?


a. A higher F-value results in a higher p-value. This would increase the possibility of having a significant difference.


b. A lower F-value results in a higher p-value. This would increase the possibility of having a significant difference.


c. A lower F-value results in a lower p-value. This would increase the probability of having a significant difference.


d. A higher F-value results in a lower p-value. This would increase the probability of having a significant difference.


e. There is no relationship between your F-value and p-value, as their relationship varies too much depending on the specific stats analysis.





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F TABLE-CRITICAL VALUES OF THE F DISTRIBUTION (CONTINUED)
Body of table contains values of (SSRmean/ SSE mean)
Top value per row is the 0.05 p level*; bottom entry is the 0.01 p level**
df FOR SSR (DEGREES OF FREEDOM OF NUMERATOR MEAN SQUARES)
10
11
12
13
14
4.49
8.53
3.63
6.23
4.77
2.85
2.74
2.66
4.44
2.59
2.49
4.20
3.89
2.54
3.78
3.69
(DEGREES OF FREEDOM OF DENOMINATOR MEAN SQUARES)
8.40
3.59
6.11
3.20
2.96
2.49
2.45
4.10
2.61
3.59
2.41
3.52
2.38
3.46
2.35
8T
8.29
3.55
6.01
3.16
2.93
4.01
2.58
2.51
2.46
2.41
2.17
2.34
ST
4.38
8.18
3.52
3.13
4.17
2.63
2.48
3.63
2.42
2.38
2.34
3.36
2.28
2.26
20
4.35
8.10
4.94
4.43
4.10
2.60
3.87
3.70
2.45
3.56
3.39
3.46
2.35
2.22
21
4.32
8.02
3.47
5.78
2.68
4.04
2.57
3.81
2.49
3.64
2.42
3.51
2.37
3.40
2.32
3.31
2.28
2.25
2.22
2.20
22
4.30
7.95
3.44
5.72
3.05
4.82
2.82
4.31
2.66
2.55
2.40
2.30
2.26
2.17
23
7.88
15 . 6
4.76
4.26
2.64
3.94
2.53
3.71
2.44
3.54
2.32
3.30
2.27
2.24
3.14
2.20
3.07
2.18
3.02
24
4.26
3 . 4
5.61
4.72
2.78
4.22
2.62
3.90
2.51
2.42
3.50
2.36
2.30
3.17
2.22
2.18
2.15
25
4.24
39
5.57
2.99
4.68
4.18
2.60
2.49
2.40
3.46
2.347
3.32
2.28
2.24
3 .13
2.20
2.14
26
4.23
2.98
2.74
7.72
3.37
5.53
4.64
2.59
4.14
3.82
2.47
3.59
2.39
3.42
2.32
3.29
2.27
3 .18
2.22
3.09
2.18
3.02
2.96
2.12
2.90
2.09
df FOR SSE.
27
4.21
7.68
3.35
5.49
2.96
4.60
4.11
3.78
2.46
3.56
3.39
2.31
2.25
2.20
3.06
2.99
2.13
2.10
2.87
4.20
3.34
2.71
2.56
7.64
5.45
2.45
3.53
2.36
3.36
2.29
3.12
2.19
3.03
2.15
2.12
2.09
2.96
2.84
2.06
2.79
29
4.18
3.33
2.93
2.55
3.73
2.43
3.50
2.35
3.33
2.28
3.20
2.22
3.09
2.18
2.14
2.93
2.10
2.08
2.05
7.60
5.42
4.04
3.00
2.87
2.81
2.77
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
3.07
2.13
2.09
2.04
7.56
5.39
4.51
3.70
3.47
3.30
2.91
2.84
2.79
2.74

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