The statement of the null hypothesis never contains an equality.
true or false
False.
The null hypothesis often contains a statement of equality. It proposes that there is no significant effect or difference for a particular statistic, meaning that any observed effect is due to random chance. In statistical hypothesis testing, the null hypothesis (H0) is generally a statement of no effect or no difference and is typically formulated using an equality sign. For example:
- In testing a new drug, the null hypothesis might be that there is no difference in effectiveness between the new drug and a placebo, which could be symbolized as H0: μ_new = μ_placebo, where μ represents the mean effectiveness.
- In testing a manufacturing process, the null hypothesis might be that the process has not changed, H0: μ_current = μ_standard.
- In a study comparing two means, the null hypothesis could be that the means are equal, H0: μ1 = μ2.
The equality in the null hypothesis sets up a specific condition that the test will evaluate. If the data suggest that the equality does not hold, the null hypothesis can be rejected in favor of the alternative hypothesis, which often contains a statement of inequality, such as "greater than," "less than," or "not equal to."