11.3 Case Study: Students heights
Suppose we want to test if the average height of a sample of students is different from the population average height (which is 165 cm).
11.3.1 Hypotheses
- H0: The average height of students is 165 cm.
- Ha: The average height of students is not equal to 165 cm.
\[\left\{\begin{matrix} H_0 & \mu=165cm \\ H_a & \mu \neq 165cm \end{matrix}\right.\]
11.3.3 Choose a Significance Level (α)
The significance level (α) is the threshold you set to determine what constitutes strong enough evidence to reject the null hypothesis. Common values for α are 0.05 or 0.01.
Significance level
11.3.4 Perform the Hypothesis Test
You can use statistical tests appropriate for your data type and research question. In this example, you can use a t-test to compare the sample mean to the population mean.
Perform t-test
11.3.5 Make a Decision
If the p-value (probability value) obtained from the test is less than α (p < α), you reject the null hypothesis. This means you have evidence to support the alternative hypothesis.
If p-value ≥ α, you fail to reject the null hypothesis. This means you don’t have enough evidence to support the alternative hypothesis.
Get the p-value from the test
p_value <- t_test$p.value
# Make a decision
if (p_value < alpha) {
cat("Reject H0: There is enough evidence to suggest that the average height is different from 165 cm.\n")
} else {
cat("Fail to reject H0: There is not enough evidence to suggest that the average height is different from 165 cm.\n")
}## Fail to reject H0: There is not enough evidence to suggest that the average height is different from 165 cm.