[Maths Class Notes] on Alternative Hypothesis Pdf for Exam

Types of Hypothesis

There are two types of statistical hypothesis.

1. Null Hypothesis: A null hypothesis can be defined as a hypothesis where there is no statistical significance between the two variables in the hypothesis. The researcher tries to disprove the hypothesis. It is denoted by H0.

2. Alternative Hypothesis: An alternative hypothesis, on the other hand, states that there is statistical significance between two variables. It is denoted by H1 or Ha.

Let’s take another example, you desire to see whether a coin will be fair and balanced. A null hypothesis might support that half of the total flips would result in Heads and half in Tails. The alternative hypothesis, on the other hand, might support that the number of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as:

H0: p = 0.5

Ha: p <> 0.5

Suppose the coin was flipped 50 times, resulting in 40 Heads and 10 Tails. Given this result, we would be inclined to reject the null hypothesis as the coin was probably not fair and balanced.

Alternative Hypothesis

The alternative hypothesis can be defined as one in which a difference between two or more variables is anticipated by the researchers. In other words, the observed pattern of the data is not due to a chance occurrence. The concept of the alternative hypothesis is a central part of formal hypothesis testing.

For example, in the development of medicine, a hypothesis can be formulated that a new treatment for a disease is better than the existing one. Therefore, this hypothesis would be called an alternative hypothesis. But if the new treatment fails to be proved correct, it will be called as a null hypothesis. To summarize, a null hypothesis is further examined to see if it’s true or false. If the null hypothesis stands rejected, the alternative hypothesis will be accepted.

Basically, the alternative hypothesis and null hypothesis are just opposite to each other. If your null hypothesis is “ there is more water in glass A than B” then your alternative hypothesis will be “there is more water in glass B than A”. The alternative hypothesis is usually a statement that a researcher thinks is true which ultimately leads you to reject the null hypothesis and replace it with the alternate hypothesis.

Examples of Alternative Hypothesis

Example 1: Ethanol’s boiling point is 173.1°F.

Solution 1:  There is a theory that states ethanol actually has a different boiling point, of over 174°F. The accepted fact that “ethanol boils at 173.1°F” is the null hypothesis while the theory “ethanol boils at temperatures of 174°F” is the alternate hypothesis.

Example 2: Elementary school students are performing at lower than average levels on standardized tests. 

Solution 2: It would be a general thought that low test scores are due to poor teacher performance. However, you have a theory that the reason behind students performing poorly is because their classroom is not as well ventilated as the other classrooms in the school. Therefore, the accepted theory that the “low test scores are due to poor teacher performance” will be the null hypothesis while the theory that states “low test scores are due to inadequate ventilation in the classroom” stands as the alternative hypothesis.

Difference Between The Null Hypothesis And Alternative Hypothesis

The difference between a null hypothesis and an alternative hypothesis is stated as follows:

1. The null hypothesis is often denoted as H0 while the alternative hypothesis is normally denoted as H1.

2.  A null hypothesis states the exact opposite of what an investigator predicts or expects whereas an alternative hypothesis makes a statement that suggests or advises a potential result or an outcome that an investigator may expect.

3. A null hypothesis basically states that there is no exact or actual relationship between the variables. An alternative hypothesis contradicts it.