Question

We know that sample statistics vary. How does a hypothesis test and p-value take into account the reality of sampling variability?

Answer 1

Sample statistic is a function of random samples. Some of common sample statistic are sample mean , sample variance etc , if our random samples vary than our sample statistic is also variable.

Hypothesis test is a statistical analysis that uses sample data to assess two mutually exclusive theories about the properties of a population.we called these theories the null hypothesis and the alternative hypothesis. A hypothesis test assesses your sample statistic and factors in an estimate of the sample error to determine which hypothesis the data support. so if the sample and sample statistic is variable than accordingly it also affects our hypothesis test.

P-values are the probability value that we would obtain the effect observed in our sample, or larger, if the null hypothesis is correct. In simpler terms, p-values tell us how strongly our sample data contradict the null. Lower p-values represent stronger evidence against the null. we use P-values in conjunction with the significance level to determine whether our data favor the null or alternative hypothesis and the p - value is calculated using the test statistic which depend upon the sample statistic so, if the sample statistic vary accordingly the test statistic and the p value varies. In general we get better results if our sample size is large.