Question

Why is the sample range always a biased estimator of dispersion in a population?

B) if the null hypothesis is not rejected in a significance test, what must be known for one to accept ho?

Answer 1

The sample mean is a random variable that is an estimator of the population mean. The expected value of the sample mean is equal to the population mean µ. Therefore, the sample mean is an unbiased estimator of the population mean.

In stage one of the hypothesis-testing process, we formulate a hypothesis called the null hypothesis. This has some special characteristics. It is a specific statement about population parameters and it provides the basis for calculating what is called a p-value. The null hypothesis is often shortened to H₀.

If the P-value is less than (or equal to) α(significance level), reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than α, do not reject the null hypothesis