Answer:
The food preferences among vole species are independent of one another.
Step-by-step explanation:
The hypothesis can be defined as follows:
<em>H</em>₀: The food preferences among vole species are independent of one another.
<em>Hₐ</em>: There is a relationship between voles and food preference.
The data provided is:
meadow voles common voles
apple slices 15 21
peanut butter-oatmeal 25 16
A Chi-square test for the Goodness of fit will be used.
The expected values are computed using the formula:
![E_{i}=\frac{\text{ith Row Total}\times \text{jth Column Total}}{N}](https://tex.z-dn.net/?f=E_%7Bi%7D%3D%5Cfrac%7B%5Ctext%7Bith%20Row%20Total%7D%5Ctimes%20%5Ctext%7Bjth%20Column%20Total%7D%7D%7BN%7D)
Consider the Excel sheet attached.
The Chi-square statistic value is 2.861.
Compute the degrees of freedom as follows:
df = (r - 1)(c - 1)
= (2 - 1)(2 - 1)
= 1
Compute the <em>p</em>-value as follows:
![p-value=P(\chi^{2}_{(1)}>2.861)=\text{CHISQ.DIST.RT(2.861,1)}=0.091](https://tex.z-dn.net/?f=p-value%3DP%28%5Cchi%5E%7B2%7D_%7B%281%29%7D%3E2.861%29%3D%5Ctext%7BCHISQ.DIST.RT%282.861%2C1%29%7D%3D0.091)
The <em>p</em>-value = 0.091 > <em>α </em>= 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that the food preferences among vole species are independent of one another.