Final answer:
The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (Ha) indicates a presumed effect or difference. An example can be the efficacy of a new drug compared to a standard treatment. The type of test used (right-tailed, left-tailed, or two-tailed) is determined by the nature of the alternative hypothesis.
Step-by-step explanation:
The null hypothesis and the alternative hypothesis are the starting points for hypothesis testing in statistics. The null hypothesis, symbolized as H0, usually represents a statement of no effect or no difference and serves as a default assumption. On the other hand, the alternative hypothesis, denoted as Ha or H1, proposes what we would consider to be true if the null hypothesis is rejected, suggesting an effect or difference.
Let's consider a simple example regarding the effectiveness of a new drug. The null hypothesis would state 'There is no difference in effectiveness between the new drug and the standard treatment'. In symbols, if we let μnew be the mean effectiveness of the new drug and μstandard be for the standard treatment, the hypothesis would be H0: μnew = μstandard. The alternative hypothesis might state 'The new drug is more effective than the standard treatment', which could be symbolized as Ha: μnew > μstandard.
The type of test (right-tailed, left-tailed, or two-tailed) depends on the alternative hypothesis. If Ha suggests the parameter is greater than the value specified in the null hypothesis, it's a right-tailed test. If Ha suggests it is less, then it's a left-tailed test. If Ha indicates the parameter is simply different (it could be either greater or less), the test is two-tailed.