The test statistic of a set of data is a value which summarises the entire data set. The choice of test statistic will vary depending upon the distribution being used. If the test statistic is in the critical region then the alternative hypothesis is accepted. Otherwise the null hypothesis is accepted.
In this case the test statistic is the number of successes obtained.
In this case the test statistic is usually the $z$-score obtained from \[z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\] where $\bar{x}$ is the sample mean, $\mu$ is the population mean being tested, $\sigma$ is the standard deviation and $n$ is the sample size. This allows us to work out the critical region straight from the standard normal distribution tables.
Alternatively, $\bar{x}$ can be used as the test statistic with the confidence interval \[\mu - k \frac{\sigma}{\sqrt{n}} < \bar{x} < \mu + k \frac{\sigma}{\sqrt{n}}\] where $k$ is obtained from the tables.
In this case the test statistic is the $t$-statistic obtained from \[t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\]
where $\bar{x}$ is the sample mean, $\mu$ is the population mean being tested, $s$ is the sample standard deviation and $n$ is the size of the sample.