---
title: "Stat. 316: Hypothesis Testing"
author: "Prof. Eric A. Suess"
date: "4/22/2024"
format: 
  html:
    self-contained: true
---

# Hypothesis Testing - Two Independent Samples

Sixteen mice were randomly assigned to a treatment group or a control group. Shown are their survival times in days, following a test surgery. Did the treatment prolong suvivial times?

| Group     | Data                         |
|-----------|------------------------------|
| Treatment | 94 197 16 38 99 141 23       |
| Control   | 52 104 146 10 50 31 40 27 47 |

Enter the data.

Notice that the Treatment has a much higher median than the Control group.

```{r}
treatment <- c(94, 197, 16, 38, 99, 141, 23)

control <- c(52, 104, 146, 10, 50, 31, 40, 27, 47)

boxplot(treatment, control, names = c("Treatment", "Control"))
```

Perform a two-sample t-test.

$H_0: \mu_1 = \mu_2$

$H_a: \mu_1 > \mu_2$

```{r}
t.test(treatment, control, alternative = "greater")

```

Since the $p \mbox{-} value = 0.1585 > 0.05$, we fail reject the null hypothesis.  There is insufficent evidence that the treatment prolongs survival times.