(a) Hypothesis:

Null Hypothesis (H0): The barking deer do not show any preference for foraging in any specific habitat type.

Alternative Hypothesis (HA): The barking deer prefer to forage in certain habitats over others.

(b) Test Type:

We can use a chi-square goodness-of-fit test to answer this research question as we want to compare the observed frequencies of barking deer foraging indifferent habitat types with the expected frequencies if there were no preference for any specific habitat type.

(c) Assumptions:

The data used in the analysis is categorical and nominal in nature.

The sample is representative of the population of barking deer in Hainan Island, China.

The sample size is large enough to meet theminimum expected frequency assumption for all cells.

(d) Hypothesis Test:

To conduct the hypothesis test, we need to calculate the expected frequencies under the null hypothesis. We assume that if the barking deer had no preference for any specific habitat, then the proportion of forage sites in each habitat type would be equal to the proportion of land occupied by each habitat type.

Expected frequency for woods = 0.048 * 426 = 20.45

Expected frequency for cultivated grassplot = 0.147 * 426 = 62.67

Expected frequency for deciduous forests = 0.396 * 426 = 168.78

Expected frequency for other habitats = (1 – 0.591) * 426 = 174.1

We can then use a chi-square goodness-of-fit test to determine whether the observed frequencies significantly differ from the expected frequencies.

The chi-square test statistic can be calculated as:

χ2 = ∑(Observed frequency – Expected frequency)^2 / Expected frequency

The degrees of freedom for this test are df = k – 1, where k is the number of categories. In this case, k = 4, so df = 3.

Using the values from the table provided:

Woods Cultivated grassplot Deciduous forests Other Total

Observed frequency 4 16 67 345 426

The chi-square test statistic is:

χ2 = [(4-20.45)^2/20.45] + [(16-62.67)^2/62.67] + [(67-168.78)^2/168.78] + [(345-174.1)^2/174.1] = 277.62

Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated chi-square value of 277.62 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that there is strong evidence to suggest that barking deer prefer to forage in certain habitats over others.

(e) Conclusion:

Based on the results of the chi-square goodness-of-fit test, we can conclude that the barking deer show a preference for foraging in certain habitat types over others. The observed frequencies significantly differ from the expected frequencies if there were no preference for any specific habitat type.