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Data analysis: hypothesis testing

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1.1 Formulating null and alternative hypotheses

In the world of scientific inquiry, you often begin with a null hypothesis (H0), which expresses the currently accepted value for a parameter in the population. The alternative hypothesis (Ha), on the other hand, is the opposite of the null hypothesis and challenges the currently accepted value.

To illustrate this concept of null and alternative hypotheses, you will look at some well-known stories and examples.

In ancient and medieval times, the widely held belief was that all planets orbited around the Earth, as the Earth was considered the centre of the universe. This idea can be considered the null hypothesis, as it represents the currently accepted value for a parameter in the population. Thus, it can be written as:

H0: All planets orbit around the Earth.

Figure 3 Solar system

In the world of business and finance, the idea that paper money must be backed by gold (the gold standard) was also a commonly held belief for a long time. This belief can be considered a null hypothesis. However, following the Great Depression, people began to question this belief and broke the link between banknotes and gold. This alternative hypothesis challenged the gold standard, and it eventually became widely accepted that the value of paper money is not necessarily equal to a fixed amount of gold. Thus, H0 and Ha statements can be written as:

H0: The value of paper money is equal to a fixed amount of gold.

Ha: The value of paper money is not equal to a fixed amount of gold.

In modern times, people generally place their trust in the value of banknotes issued by central banks or monetary authorities, which are backed by a strong government. This belief can be considered a null hypothesis. However, digital currency, such as Bitcoin, has emerged as an alternative to traditional paper money. Bitcoin is not backed by any central bank or monetary authority, and transactions involving Bitcoin are verified by network nodes using cryptography and recorded in a blockchain. This alternative hypothesis challenges the belief that the value of paper money is solely based on people's trust in central banks or monetary authorities. Thus, H0 and Ha statements can be written as:

H0: The value of paper money is equal to people’s trust in central banks or monetary authorities.

Ha: The value of paper money is not equal to people’s trust in central banks or monetary authorities.

In conclusion, the alternative hypothesis always challenges the idea expressed in the null hypothesis. By testing the null hypothesis against the alternative hypothesis, you can determine which idea is more supported by the available data. The alternative hypothesis is often referred to as a ‘research hypothesis’ because it initiates the motivation and opportunities for further research.

Let’s return to the first example given in Section 1. If you see that your friends and relatives make more or less than £26,000 annually on average, perhaps you should question the widely accepted proposition of £26,000 as the average annual salary in the UK. This will enable you to develop an alternative hypothesis:

Ha: Average annual salary in the UK is not equal to £26,000.

The following activity will test your knowledge of null and alternative hypotheses.

Activity 1 Null hypothesis versus alternative hypothesis

Timing: Allow approximately 10 minutes to complete this activity

Read the following statements. Can you develop a null hypothesis and an alternative hypothesis?

‘It is believed that a high-end coffee machine produces a cup of caffè latte with an average of 1 cm of foam. The hotel employee claims that after the machine has been repaired, it is no longer able to produce a cup of caffè latte with 1cm foam.’

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Discussion

H0: a coffee machine makes a cup of caffè latte with 1cm foam on average.

Ha: a coffee machine cannot make a cup of caffè latte with 1 cm foam on average.

If you have developed the hypotheses H0 and Ha as mentioned in the discussion to Activity 1, you have shown that you are familiar with the structure of different types of hypotheses. However, in the next section you will explore the concept of hypothesis formulation further.