Hermit crabs live in shells, but they don't grow the shellsthemselves. They find an abandoned snail shell and make it theirhome. They inhabit shells of different snail species, but it's notclear if the hermit crabs choose shells of different speciesrandomly or if they have a preference for certain snailspecies.
We can't just collect a bunch of hermit crabs and then concludethat the snail shell with the highest prevalence is the mostpreferred, because it might be the case that that snail species issimply more common. Instead, it makes more sense to collect a bunchof shells, and determine if they are occupied or unoccupied by acrab. If crabs have no preference, then the ratio of occupied tounoccupied should be the same across snail species.
For three snail species in the area, shells were collected andit was recorded whether they were inhabited by a hermit crab. Thedata:
| Occupied | Vacant |
| Species 1 | 47 | 42 |
| Species 2 | 10 | 41 |
| Species 3 | 125 | 49 |
The question of interest is: do hermit crabs care about thespecies of shell they inhabit?
Step 2: State the null hypothesis.
Step 3: State the alternative hypothesis.
Step 4: What is the correct level of alpha?
Step 5: Which statistical test are you using?
Step 6: What is the value of the test statistic?
Step 6 continued: How many degrees of freedom in this test?
Step 7: What is the critical value for the test statistic?
Step 8: How does the test statistic compare to the criticalvalue?
Step 9: Based on this comparison, do you accept or reject yournull hypothesis?
Step 10: What do you conclude from this analysis?
