Which of these directly allows you to test a hypothesis? Point estimate Standard error Test statistic Confidence interval

1. **Point Estimate** A point estimate is a single value that is used to approximate a population parameter. For example, the sample mean \( \bar{x} \) is a point estimate for the population mean \( \mu \). Although useful, it does not itself provide a direct mechanism to test a hypothesis. 2. **Standard Error** The standard error measures the variability or spread of a sampling distribution. It helps in determining how precise a point estimate is, but on its own, it does not allow you to test a hypothesis, though it is used in the computation of the test statistic. 3. **Test Statistic** A test statistic is a value calculated from sample data that is used directly to test a hypothesis. For example, in a one-sample \( t \)-test, the test statistic is computed as \[ t = \frac{\bar{x} - \mu_0}{SE} \] where \( \bar{x} \) is the sample mean, \( \mu_0 \) is the hypothesized population mean, and \( SE \) is the standard error. This statistic is then compared to a critical value or used to compute a \( p \)-value to decide whether to reject the null hypothesis. 4. **Confidence Interval** A confidence interval provides a range of values which is likely to contain the population parameter. While it is very useful for estimation and provides insight into the uncertainty associated with an estimate, it is not directly used to test a hypothesis. The item that directly allows you to test a hypothesis is the **Test Statistic**.