Marine biologists are studying the spatial distribution of giant clams (Tridacna gigas) across a reef flat in the Indo-Pacific.
They categorise the reef flat into three distinct substrate types: sandy seabed, coral rubble, and live coral.
In a selected transect area, the biologists record every giant clam found on each of these three substrate types. The observed frequencies are shown in the table below:
| Substrate Type | Number of giant clams observed |
|---|---|
| Sandy seabed | 40 |
| Coral rubble | 92 |
| Live coral | 108 |
The null hypothesis for this study is that the substrate type has no effect on the distribution of the giant clams, meaning they are distributed uniformly across the three substrate types.
Calculate the χ2 \chi^2\,χ2 value for this data using the formula:
χ2=∑(O−E)2E \chi^2 = \sum \frac{(O - E)^2}{E} χ2=∑E(O−E)2The critical value for χ2 \chi^2\,χ2 at the 5% significance level (p=0.05p = 0.05p=0.05) with 2 degrees of freedom is 5.991. Discuss what can be concluded from this comparison.
