Overview
Consider the following situation-
“A scientist wants to test whether a new vaccine is really more effective for controlling the disease than an old vaccine.”
In this case the scientist is interested in making inference about the population parameter, however the scientist is not interested in estimating the value of parameter, but he is interested in testing a claim about the value of population parameter.
Such claims are postulated in terms of hypothesis.
To test the hypothesis, we draw a sample from a large population and make certain decisions about the population on the basis of sample information we draw from the population.
These assumptions are called “statistical hypotheses.”
Null hypothesis and alternative hypothesis
According to Prof. R.A. Fisher,
“A null hypothesis is a hypothesis which is tested for possible rejection under the assumption that it is true”
“The hypothesis which complements the null hypothesis is called the alternative hypothesis.”
The null hypothesis is denoted by H0 and the alternative hypothesis is denoted by H1.
For example, Suppose a man goes to a car agency to buy a car, where the manager of the agency claims that the car gives the average mileage of 30km/liter.
And now the customer wants to test the claim, then he proceeds as follows-
Here the claim is =30 km/liter and its complement is μ ≠ 30km/liter Since claim μ = 30km/liter contains equality sign so we take it as a null hypothesis and complement μ ≠ 30km/liter as an alternative.
He makes the null and alternative hypothesis as follows-
H0: μ = 30km/liter and H1:μ ≠ 30km/liter.
Critical region
“A region in the sample space in which if the calculated value of the test statistic lies, we reject the null hypothesis then it is called critical region or rejection region.”
Type-1 and Type-2 errors
As we know that if the test statistic value lies inside the critical region then we reject the null hypothesis and if it lies in the non-rejection region then we can not reject the null hypothesis.
A random sample taken from the population may or may not be a good representative of the given population.
We come across the two types of errors while testing hypotheses.
| Decision | H0 true | H1true |
| Reject | TYPE-I ERROR | Correct decision |
| Don’t reject | Correct decision | TYPE-II ERROR |
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