Final answer:
Hypothesis testing involves comparing a null hypothesis, which suggests no effect, and an alternative hypothesis, which suggests an effect or difference.
Step-by-step explanation:
When conducting hypothesis testing, null hypothesis (H0) and alternative hypothesis (Ha) are formulated to make inferences about a population based on sample data. The null hypothesis is typically a statement of no effect or no difference, while the alternative hypothesis reflects the presence of an effect or difference.
- For the drug safety example, the null hypothesis (H0) might state that the drug is unsafe, while the alternative hypothesis (Ha) would state that the drug is safe. A Type II error in this scenario is when we fail to reject the null hypothesis when the drug is actually safe, which corresponds to option b.
- For the number of jobs and change in years example, if we are testing for independence, the null hypothesis (H0) would propose that the number of jobs is independent of the years, while the alternative hypothesis (Ha) would suggest they are not. The degrees of freedom would be calculated based on the number of categories minus one for each variable involved.
Similarly, in a test of homogeneity about early and regular applications, the null hypothesis (H0) states that the distributions of accepted applications are the same, while the alternative hypothesis (Ha) states that they are different. Degrees of freedom, the test statistic, the graph of the p-value, and a conclusion are all part of the results of this test.