Hypothesis Test of Hypothetical Population Mean

Methods of statistical inference

Recall from previous lessons that to estimate the unknown population mean, we may employ two methods of statistical inference:

• Null hypothesis testing
• Confidence interval construction

In this lesson, we focus on the first method.

We know some countries grow rapidly in some years but slowly in other years, while other countries tend to grow slowly for a very long time. As a result, it’s often difficult to guess the average growth rate in the population. Suppose scholars have reasons to believe and hypothesize that the population’s average growth rate is 3%. In contrast, our sample estimate is 0.023 or 2.3%. The question then becomes the following: given the sampling error and noise, is 2.3% statistically the same as 3% or not? In other words, is their difference a statistical error or a fact?