1.3 Hypothesis formulation

While these hypotheses demonstrate a basic understanding of hypothesis structure, we can refine them further to align more closely with statistical conventions. In hypothesis formulation, we typically express the null hypothesis (H₀) in terms of the population mean (µ), which represents the average value in the population. The symbol µ is commonly used to denote this population mean.

To illustrate this concept, let us revisit our earlier example of the average UK salary. The widely accepted belief that the average UK salary is £26,000 per year can be expressed statistically as:

• H₀: µ = £26,000

Here, µ represents the population mean salary. The alternative hypothesis (H₁), which challenges this belief, can be expressed as:

• H₁: µ ≠ £26,000

This formulation clearly shows that H₁ is the opposite of H₀, reflecting its purpose of challenging the widely held belief represented by the null hypothesis.

Applying this more precise formulation to our caffè latte foam example, we can express the hypotheses as:

• H₀: µ = 1cm foam
• H₁: µ ≠ 1cm foam

In this case, µ represents the population mean for the height of foam in a caffè latte. The null hypothesis states that this mean is exactly 1cm, while the alternative hypothesis suggests a departure from this widely accepted belief. Note that H₀ and H₁, when taken together, cover all possible outcomes regarding the foam height.

This approach to hypothesis formulation offers several advantages in business decision making. Firstly, it provides a clear, quantifiable statement that can be tested statistically. Secondly, it allows for precise measurement and analysis, enabling businesses to make data-driven decisions with confidence. Finally, it sets the stage for more advanced statistical analyses, such as determining the significance of any observed differences from the hypothesised mean.