Homework SourseE jugularis is a type of hummingbird that lives in the fores
E. jugularis is a type of hummingbird that lives in the forest preserves of the Caribbean island of Saint Lucia. The males and the females of this species have bills that are shaped somewhat differently. Researchers who study these birds thought that the bill shape might be related to the shape of the flowers that they visit for food. The researchers observed 49 females and 21 males. Of the females, 20 visited the flowers of H. bihai, while none of the males visited these flowers. Display the data in a two-way table and perform the chi-square test. Summarize the results and give a brief statement of your conclusion. Your two-way table has a count of zero in one cell. Does this invalidate your significance test? Explain why or why not.
Solution
Null hypothesis H0 : the bill shape not related to the shape of the flowers that they visit for food
Alternative hypothesis: H1 : the bill shape related to the shape of the flowers that they visit for food
Observed Frequencies
Column variable
Calculations
Row variable
female
male
Total
fo-fe
visited
20
0
20
6
-6
not vid
29
21
50
-6
6
Total
49
21
70
Expected Frequencies
Column variable
Row variable
female
male
Total
(fo-fe)^2/fe
visited
14
6
20
2.571429
6
not vid
35
15
50
1.028571
2.4
Total
49
21
70
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841
Chi-Square Test Statistic
12
Calculated chi square =12
Table value of chi square at 0.05 level=3.841
The calculated value > table value
Null hypothesis is rejected.
We conclude that the bill shape is related to the shape of the flowers that they visit for food.
The two-way table has a count of zero in one cell. This does not invalidate your significance test because the expected value for all the cells are greater than 5.
| Observed Frequencies | ||||||
| Column variable | Calculations | |||||
| Row variable | female | male | Total | fo-fe | ||
| visited | 20 | 0 | 20 | 6 | -6 | |
| not vid | 29 | 21 | 50 | -6 | 6 | |
| Total | 49 | 21 | 70 | |||
| Expected Frequencies | ||||||
| Column variable | ||||||
| Row variable | female | male | Total | (fo-fe)^2/fe | ||
| visited | 14 | 6 | 20 | 2.571429 | 6 | |
| not vid | 35 | 15 | 50 | 1.028571 | 2.4 | |
| Total | 49 | 21 | 70 | |||
| Data | ||||||
| Level of Significance | 0.05 | |||||
| Number of Rows | 2 | |||||
| Number of Columns | 2 | |||||
| Degrees of Freedom | 1 | |||||
| Results | ||||||
| Critical Value | 3.841 | |||||
| Chi-Square Test Statistic | 12 |
