1.2 Population mean (µ)

As you have seen so far in Section 1, the formulation of H₀ is based on widely accepted beliefs, which can also be interpreted as the population mean (µ), representing the average value in the population (where µ is the symbol for a population mean).

To illustrate this point, consider the example of the average UK salary, which is ‘widely believed’ to be £26,000 per year. In this case, µ is equivalent to £26,000, which can be expressed as:

H₀: µ = £26,000

As H₀ and H_a are always opposite (i.e. since the purpose of H_a is to challenge the belief of H₀), you can also express H_a as:

H_a: µ ≠ £26,000.

If you revisit the caffè latte foam example from Activity 1, H₀ and H_a can also be expressed as:

H₀: µ = 1cm foam (representing the population mean for the height of foam in a caffè latte)

H_a: µ ≠ 1cm foam (indicating a departure from the widely accepted belief about the population mean).

In summary, the process of hypothesis formulation is a critical step in business decision making. It involves setting up the null hypothesis (H₀), which represents the widely accepted belief or the status quo (or µ), and the alternative hypothesis (H_a), which challenges the belief and suggests the possibility of a significant difference. A clear understanding of the concept of hypothesis formulation is crucial for accurate business decision making.

Having discussed how hypotheses are formulated, you will now turn your attention to how to test them. In the following sections, you will look at test statistics and alpha levels, which play a critical role in determining the statistical significance of a hypothesis test.