Null Hypothesis (H₀): - The null hypothesis represents a statement that is true and accepted by the default. - It is a statement about the population fr...
Null Hypothesis (H₀):
The null hypothesis represents a statement that is true and accepted by the default.
It is a statement about the population from which the sample was drawn.
The null hypothesis is usually denoted by a symbol, such as H₀.
Alternative Hypothesis (H₁):
The alternative hypothesis represents a statement that is not true and must be rejected by the default.
It is a statement about the population from which the sample was drawn.
The alternative hypothesis is denoted by a symbol, such as H₁.
Example:
H₀: p = 0.5 (The population proportion is 50%)
H₁: p ≠ 0.5 (The population proportion is not 50%)
Importance of Null and Alternative Hypotheses:
Null hypothesis and alternative hypothesis form the basis of hypothesis testing.
If the null hypothesis is true, we reject the alternative hypothesis.
If the null hypothesis is false, we fail to reject the alternative hypothesis.
The probability of rejecting the null hypothesis when it is true (Type I error) is denoted by a level of significance (α).
The probability of making a Type II error (failing to reject a false null hypothesis) is denoted by a power (1 - α).
Null and alternative hypotheses are crucial in hypothesis testing, as they provide a framework for determining the evidence and making decisions based on the collected data