Answer:
1.2 Test statistics
A test statistic is a numerical summary of the data that is compared to what would be expected under the null hypothesis. Test statistics can take on many forms such as the z-tests (usually used for large datasets) or t-tests (usually used when datasets are small).
1.3 z-tests
The z-statistic is a measure of how much an observed statistic differs from an expected statistic put forward by the null hypothesis. It is computed as
z=observed−expectedSE
In computing the z-statistic, the SE used is not the standard error of the observed data, but the standard error for the null. To be more precise, the SE in this formula is computed from the null’s SD, if given. However, in many cases (such as in this working example) the null’s SD can only be estimated from the observed data’s SD.
For example, the z-statistic for our scenario i
Ho <- 28.5
z <- (mean.x - Ho) / SE.x
where SE.x is the observed sample’s standard error. In our working example, z’s value of 2.74 indicates that the sample mean is 2.74 SE ’s away from the hypothesized value.
