As a statistical expert with a deep understanding of hypothesis testing and statistical distributions, I can provide a comprehensive answer to your question about the relationship between the test statistic and the Z value.
Firstly, it's important to clarify what we mean by a "test statistic." In the context of hypothesis testing, a test statistic is a numerical value calculated from sample data. It is used to determine whether there is enough statistical evidence to reject the null hypothesis. The choice of test statistic depends on the type of hypothesis test being conducted. For example, in a t-test, the test statistic might be the t-value, while in a chi-square test, it could be the chi-square value.
Now, let's talk about the Z value. The Z score, or Z value, is a specific type of test statistic used primarily in the context of the normal distribution. It measures the number of standard deviations a data point is from the mean. In the context of hypothesis testing, the Z value can be used as a test statistic when the sample size is large, and the population standard deviation is known. This is because, with large sample sizes, the sampling distribution of the mean tends to approximate a normal distribution, even if the underlying population distribution is not normal, due to the Central Limit Theorem.
However, it's not accurate to say that the test statistic is always the Z value. The Z value is just one possible test statistic, and its use is contingent on certain conditions being met. For instance, if the sample size is small or the population standard deviation is unknown, a Z test may not be appropriate, and another test statistic, such as the t-value, might be used instead.
Additionally, the Z value and the p-value are related but distinct concepts. The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from your sample data, assuming the null hypothesis is true. It provides a measure of the strength of the evidence against the null hypothesis. A low p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis and is often used as a criterion for rejecting the null hypothesis.
In contrast, the Z value is a measure of how many standard deviations away from the mean a particular data point lies. It is used to determine the likelihood of observing a particular data point under the assumption that the null hypothesis is true. When conducting a Z test, you compare the calculated Z value to a critical value from the standard normal distribution to determine whether to reject the null hypothesis.
Both the Z value and the p-value are associated with the standard normal distribution, but they serve different purposes in hypothesis testing. The Z value helps to standardize the data and make comparisons across different studies, while the p-value quantifies the strength of the evidence against the null hypothesis.
In summary, while the Z value can be used as a test statistic under certain conditions, it is not the only test statistic, nor is it always the appropriate one. The choice of test statistic should be based on the specific requirements of the hypothesis test, including the sample size, the distribution of the data, and whether the population parameters are known.

read more >>

The Z score is a test of statistical significance that helps you decide whether or not to reject the null hypothesis. The p-value is the probability that you have falsely rejected the null hypothesis. Z scores are measures of standard deviation. ... Both statistics are associated with the standard normal distribution.read more >>