(a) A district biostatistician investigating declining uptake of immunization decides to take a sample of 100 households in the districts and interviews selected members of the household. Explain ho the biostatistician can employ the following statistical techniques to identify the likely factors contributing to the decline in immunization. (i) Test of significance-: (ii) Hypothesis testing (iii) Statistical inference.

Test of Significance:

A test of significance is a statistical method used to determine if thebobserved differences or correlations in data are statistically significant or if they happened by chance, as:

1. Formulate null and alternative hypotheses: Start by defining a null hypothesis (H₀) and an alternative hypothesis (H_a). The null hypothesis typically states that there is no significant effect or difference, while the alternative hypothesis suggests that there is a significant effect or difference. For example:

Null Hypothesis (H₀): There is no significant difference in immunization rates among rich and poor people.

Alternative Hypothesis (H_a): There is a significant difference in immunization rates among rich and poor people.

1. Select the appropriate test statistic: Depending on the nature of the data and the research question, choose an appropriate statistical test. Common tests for different scenarios include t-tests, ANOVA (Analysis of Variance), regression analysis etc.

2. Collect data and calculate the Test statistic: Collect data from the 100 households. The data must include information on immunization rates and potential correlated factors such as demographic variables like age, income, education etc., geographical location and access to healthcare. Calculate the test statistic based on the chosen test. The test statistic will indicate whether there is a significant difference or relationship among the variables.

3. Choose a significance level (alpha), generaly set at 0.05 (5%) or lower. This represents the threshold below which you will consider the results statistically significant.

4. Use a statistical software or calculators to perform the test with the collected data. The output will include the test statistic and the p-value.

5. Interpret the Results: Compare the p-value to the chosen significance level (). If the p-value is less than or equal to alpha (p ≤ ), you reject the null hypothesis. This indicates that there is a statistically significant difference or relationship.

6. Draw Conclusions: Based on the results, draw conclusions about the factors contributing to the decline in immunization. If the null hypothesis is rejected, it suggests that there is a significant factor or factors influencing immunization rates. Further analysis may be needed to identify which specific factors are contributing.