Formulate Hypotheses For Hermit Crabs' Shell Exchanges ✓ Solved

Formulate hypotheses for hermit crabs' shell exchanges experiment

Hermit crabs fight for ownership of shells. Fights are initiated when one crab raps on the shell of another with its big claw. An exchange of shells occurs approximately 50% of the time. Investigators wish to see if the rapping force helps decide the issue. They set up an experiment with a rubberized shell, which would dampen the force of the rapping. They reason that the reduced force should result in fewer exchanges of shells. They then observed 59 fights to see how many shell exchanges occurred. What null and alternative hypotheses should the investigators use?

Sample Paper For Above instruction

The experiment conducted by the investigators aims to determine whether the rapping force employed during hermit crab fights influences the likelihood of shell exchanges. The central premise is that the physical force exerted through rapping on shells might play a decisive role in the outcome of such disputes. Given that in normal conditions, approximately 50% of fights lead to an exchange of shells, the investigators hypothesize that dampening the force will lead to a decrease in these exchanges.

Formulating the hypotheses involves setting a null hypothesis (H₀) that represents the default or status quo, and an alternative hypothesis (H₁) that reflects the anticipated effect of the rubberized shell intervention. The null hypothesis should state that the rapping force has no effect on the proportion of fights resulting in shell exchanges. Mathematically, this can be expressed as:

H₀: The proportion of shell exchanges in fights with dampened force is equal to 50%, or p = 0.50.

Conversely, the alternative hypothesis posits that the dampening of the force decreases the rate of shell exchanges. Therefore, it should be formulated as:

H₁: The proportion of shell exchanges in fights with dampened force is less than 50%, or p < 0.50.

This set of hypotheses encapsulates the researchers' expectation that reducing the force of rapping should diminish the likelihood of shell exchanges, aligning with the hypothesis that force is a key determinant in disputing outcomes.

Testing these hypotheses would involve analyzing the observed data from the 59 fights, specifically the number of exchanges that occurred, and comparing the sample proportion to the null hypothesis value of 0.50 using an appropriate statistical test, such as a one-proportion z-test. If the observed proportion is significantly less than 0.50 at a chosen significance level (e.g., α = 0.05), then the null hypothesis can be rejected, supporting the conclusion that dampening the force reduces shell exchanges.

In conclusion, the hypotheses are formulated to statistically evaluate whether the interference with the rapping force influences the outcome of hermit crab fights, specifically the rate of shell exchanges. Such analysis will clarify whether physical force plays a significant role in dispute resolution among hermit crabs, testing the investigators' supposition that dampening the force results in fewer exchanges.

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