# 1. Introduction

This R program performs an F-test, which is used to compare the variances of two populations to ascertain if they are equal. It's particularly useful in the analysis of variance (ANOVA).

# 2. Program Steps

1. Define two sample datasets representing two populations.

2. Calculate the variances of these two datasets.

3. Perform the F-test to compare the variances.

4. Print the results of the F-test.

# 3. Code Program

``````# Step 1: Define two sample datasets
sample1 <- c(15, 20, 25, 30, 35)
sample2 <- c(20, 22, 24, 26, 28)

# Step 2: Calculate the variances of the datasets
variance1 <- var(sample1)
variance2 <- var(sample2)

# Step 3: Perform the F-test
f_test_result <- var.test(sample1, sample2)

# Step 4: Print the results of the F-test
print("F-test results:")
print(f_test_result)

``````

### Output:

```F-test results:
[F-test output including F-statistic and p-value]
```

### Explanation:

1. sample1 <- c(15, 20, 25, 30, 35), sample2 <- c(20, 22, 24, 26, 28): Initializes two sample datasets.

2. var(sample1), var(sample2): Calculates the variances of each sample.

3. var.test(sample1, sample2): Conducts the F-test to compare the variances of the two samples.

4. print("F-test results:"), print(f_test_result): Prints the results of the F-test, including the F-statistic and p-value. The p-value helps determine whether the variances are significantly different.