A t-test is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. In R, you can perform one-sample t-tests and paired t-tests using the t.test() function. Here’s how to conduct these t-tests with examples:

- One-Sample T-Test:

The one-sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized population mean.

# Example: One-sample t-test

# Hypothesized population mean: 50

# Sample data: Exam scores

scores ← c(56, 62, 58, 53, 60, 57, 59, 61, 55, 54)

# Perform one-sample t-test

t_test_result ← t.test(scores, mu = 50)

# Print the t-test result

print(t_test_result)

A t-test is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. In R, you can perform one-sample t-tests and paired t-tests using the t.test() function. Here’s how to conduct these t-tests with examples:

- One-Sample T-Test:

The one-sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized population mean.

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# Example: One-sample t-test

# Hypothesized population mean: 50

# Sample data: Exam scores

scores ← c(56, 62, 58, 53, 60, 57, 59, 61, 55, 54)

# Perform one-sample t-test

t_test_result ← t.test(scores, mu = 50)

# Print the t-test result

print(t_test_result)

- Paired T-Test:

The paired t-test is used when you have two related samples (e.g., before and after measurements) and want to determine if there is a significant difference in means.

# Example: Paired t-test

# Sample data: Before and after weights of individuals

before ← c(150, 155, 160, 145, 170)

after ← c(148, 157, 159, 143, 167)

# Perform paired t-test

paired_t_test_result ← t.test(before, after, paired = TRUE)

# Print the paired t-test result

print(paired_t_test_result)

In both examples, the t.test() function calculates the t-test and provides various output, including the t-statistic, degrees of freedom, p-value, and confidence interval. The mu parameter in the one-sample t-test specifies the hypothesized population mean.

Remember that when interpreting the results, you’ll typically focus on the p-value. If the p-value is less than a chosen significance level (e.g., 0.05), you may conclude that there is a significant difference between the sample means.

These examples demonstrate how to perform one-sample and paired t-tests in R using the t.test() function. The t-test is a common tool for hypothesis testing and determining whether observed differences are statistically significant.