**Core Concept**
The question requires the application of statistical analysis to determine if there is a significant association between consuming herbal tea and the development of the common cold. This involves comparing the proportions of individuals who developed a cold and those who did not develop a cold in relation to their consumption of herbal tea.

**Why the Correct Answer is Right**
The Chi-square test is a non-parametric test used to determine if there is a significant association between two categorical variables. In this case, the variables are "consumption of herbal tea" (categorical) and "development of the common cold" (categorical). The Chi-square test calculates the likelihood of observing the given frequency distribution by chance, and it provides a p-value that indicates the probability of observing the observed association or a more extreme one, assuming that there is no real association between the variables. The given data can be represented in a 2x2 contingency table, which is suitable for the Chi-square test.

**Why Each Wrong Option is Incorrect**

**Option A:** The 'Z' test is used to compare the means of two groups, which is not applicable in this scenario since the data is categorical, not numerical.

**Option C:** Student's t-test (paired) is used to compare the means of two related groups, which is not relevant here as the data is categorical and not paired.

**Option D:** Student's t-test (unpaired) is used to compare the means of two independent groups, which is not suitable for this scenario since the data is categorical, not numerical.

**Clinical Pearl / High-Yield Fact**
When analyzing categorical data, it's essential to use the appropriate statistical test to avoid Type I or Type II errors. The Chi-square test is a valuable tool for determining associations between categorical variables, and it's widely used in epidemiological and public health studies.

**✓ Correct Answer: B. Chi square test**