Hypothesis testing = a statistical method used to decide whether there is enough evidence in data to support a specific claim about a population.

Test 2 competing hypotheses:

\[ H_0: \mu = \mu_0 \]

\[ H_a: \mu \neq \mu_0 \]

where \(\mu\) is the true population mean..

p-value = the probability of observing data at least as extreme as the sample result, assuming the null hypothesis is true.

\[ p = P(\text{data} \mid H_0) \]

A small p-value provides evidence against \(H_0\).

Suppose the average exam score ~ 75.

We collect a random sample of exam scores and want to test whether the true mean score differs from 75.

t_test_result <- t.test(scores, mu = 75)
t_test_result

## 
##  One Sample t-test
## 
## data:  scores
## t = 0.95166, df = 9, p-value = 0.3661
## alternative hypothesis: true mean is not equal to 75
## 95 percent confidence interval:
##  73.89835 77.70165
## sample estimates:
## mean of x 
##      75.8