Question

Assume you are a social scientist and wish to compare two distinct groups of people (e.g., men vs women; old vs young; those with college degree versus those without, etc.) with respect to a subject of your choosing (e.g., social, religious, political issues, choice of COVID-19 vaccine, etc.). State the question you wish to study. Then, form the null and alternative hypotheses. Describe the process you would use to test your hypothesis including the test statistic and the level of significance you would use.

Answer 1

To compare two distinct groups, formulate a hypothesis and conduct hypothesis testing. State the question, form the null and alternative hypotheses, define the random variable, calculate the test statistic and p-value, make a decision based on the chosen significance level, and consider Type I and Type II errors.

Step-by-step explanation:

To compare two distinct groups of people with respect to a subject, you need to formulate a hypothesis and conduct hypothesis testing. Here is the step-by-step process:

1. State the question you wish to study. For example, you could ask: 'Do men and women have different preferences for COVID-19 vaccines?'
2. Formulate the null hypothesis (H0) and alternative hypothesis (Ha). In this example, H0 could be: 'There is no difference in vaccine preferences between men and women.' Ha could be: 'There is a difference in vaccine preferences between men and women.'
3. Define the random variable, P', which represents the proportion of each group who prefer a specific vaccine.
4. Calculate the test statistic, which depends on the type of data and hypotheses being tested. For example, if you have categorical data and want to compare proportions, you could use the z-test or chi-square test.
5. Calculate the p-value, which measures the probability of obtaining the observed data or more extreme if the null hypothesis is true.
6. Make a decision based on the p-value and the level of significance you choose. For example, if the p-value is less than your chosen significance level (e.g., 0.05), you reject the null hypothesis.
7. The Type I error refers to rejecting the null hypothesis when it is true. The Type II error refers to failing to reject the null hypothesis when it is false.