# 1. Introduction

This R program performs a Chi-square test, which is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It's commonly used in hypothesis testing.

# 2. Program Steps

1. Define a contingency table or observed frequencies.

2. Perform the Chi-square test on the data.

3. Print the results of the Chi-square test.

# 3. Code Program

# Step 1: Define a contingency table / observed frequencies
# Example data (2x2 table)
observed_frequencies <- matrix(c(10, 20, 20, 30), nrow = 2)

# Step 2: Perform the Chi-square test
chi_square_result <- chisq.test(observed_frequencies)

# Step 3: Print the results of the Chi-square test
print("Chi-square test results:")
print(chi_square_result)

### Output:

Chi-square test results:
[Chi-square test output including Chi-square value and p-value]

### Explanation:

1. matrix(c(10, 20, 20, 30), nrow = 2): Creates a matrix representing the observed frequencies in a contingency table format.

2. chisq.test(observed_frequencies): Performs the Chi-square test on the observed frequencies. This function calculates the Chi-square statistic and its associated p-value.

3. print("Chi-square test results:"), print(chi_square_result): Prints the results of the Chi-square test, including the test statistic and p-value, which indicate whether the observed frequencies differ significantly from expected frequencies under the null hypothesis.