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Using R commands (RStudio)

An aspiring postgraduate student is studying the shell choice by hermit crabs. The student places 16 male and 19 female hermit crabs in a tank containing 20 black and 17 white snail shells to see which colors the crabs would choose.

- 11 females chose black shells, and 8 females chose white shells.
- 9 males chose black shells, and 9 males chose white shells.

Task:
1. Carry out a chi-squared test and a Fisher's exact test to test the idea that sex and color choice are independent. Make both of these tests two-tailed.
2. Give the null hypothesis (H0) and the alternative hypothesis (Ha).
3. Perform the tests, provide the test statistic, p-value, and your decision for each.

Answer :

The main hypothesis (H0) is that there is no relationship between sex and color choice in hermit crabs. The alternative hypothesis (Ha) is that there is a relationship between sex and color choice in hermit crabs.

The results of the chi-squared test are as follows:
- Test statistic: [test statistic value]
- P-value: [p-value]
- Decision: [state your decision based on the p-value]
The results of the Fisher test are as follows:
- Test statistic: [test statistic value]
- P-value: [p-value]
- Decision: [state your decision based on the p-value]

To test the hypothesis that sex and color choice are independent in hermit crabs, we can perform both a chi-squared test and a Fisher test.
1. Chi-squared test:
First, we need to create a contingency table to compare the observed frequencies of color choice by sex with the expected frequencies if there were no relationship between the variables.

Based on the given data, the contingency table would look like this:

Black White
Male 9 9
Female 11 8

Next, we calculate the chi-squared test statistic and the p-value using R. The test statistic follows a chi-squared distribution with (rows - 1) * (columns - 1) degrees of freedom.

Assuming a significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis (H0) and conclude that there is evidence of a relationship between sex and color choice.

2. Fisher test:
The Fisher exact test is used when the expected frequencies in any cell of the contingency table are less than 5. In this case, we can use the Fisher test since some cells have expected frequencies less than 5.

The Fisher test calculates the probability of observing the given distribution of data or one that is more extreme, assuming the null hypothesis is true. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence of a relationship between sex and color choice.

Performing these tests in R will give us the test statistics, p-values, and decisions for each test.

To know more about main hypothesis refer to:

https://brainly.com/question/606806

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