## 2.2 Carrying out the test: Two-sample test of proportions

We are now ready to carry out the one-sample test of proportions to test whether the proportion of social media users who use Facebook more than once per day is different from 0.73. The results o the test are as follows:

```
2-sample test for equality of proportions with continuity correction
data: c(154, 320) out of c(220, 416)
X-squared = 3.2776, df = 1, p-value = 0.07023
alternative hypothesis: two.sided
95 percent confidence interval:
-0.145548179 0.007086641
sample estimates:
prop 1 prop 2
0.7000000 0.7692308
```

We note the following:

- The
**test statistic**is equal to 3.2776 **\(p\)-value**is equal to 0.07023. Since this is larger than \(\alpha = 0.05\), we cannot reject \(H_0\). However, we can say that this is 'close to significant' since the \(p\)-value is not too much greater than 0.05 (i.e. it is less than 0.1)- The
**95% confidence interval**for the difference between \(p_1\) and \(p_2\) is (-0.1455, 0.0071), meaning that we are 95% confident that the difference in proportion between groups is within the interval (-0.1455, 0.0071). Since the interval includes 0, we cannot reject \(H_0\) at the \(\alpha = 0.05\) level of significance. - The
**sample proportions**are \(\hat{p}_1 = 0.7\) and \(\hat{p}_2 = 0.7692\) (under`prop 1`

and`prop 2`

).

We can, in fact, carry out hypothesis tests to test for differences in proportions between more than two groups. We will be considering such hypothesis tests in the next topic.