A chi-sqaure test would be most appropriate for testing which one of the following hypotheses?
**Question:** A chi-square test would be most appropriate for testing which one of the following hypotheses?
A. The distribution of a particular disease among different age groups is the same as that of the general population.
B. There is a significant difference in the height of males and females in a population.
C. The distribution of a particular disease is independent of the gender of the individual.
D. The prevalence of a specific gene is equal in two populations.
**Core Concept:** A chi-square test is a statistical method used to test hypotheses about the association between categorical variables, specifically comparing observed versus expected frequencies in a contingency table.
**Why the Correct Answer is Right:** The correct answer is C. The hypothesis states that the distribution of a particular disease is independent of the gender of the individual. In other words, the hypothesis tests whether the disease prevalence is the same in males and females. This is appropriate for a chi-square test because it involves comparing observed and expected frequencies in a 2x2 contingency table, evaluating the association between the disease status and gender.
**Why Each Wrong Option is Incorrect:**
A. Chi-square test is not suitable for testing the hypothesis that the distribution of a particular disease among different age groups is the same as that of the general population. This hypothesis involves comparing the age distribution in a study group to a reference population, which requires a different statistical method, such as the Z-test or t-test, depending on whether the variables are categorical or continuous.
B. The chi-square test is inappropriate for determining the significant difference in height between males and females. This test is specifically designed for categorical variables, whereas the difference in height is a continuous variable and should be analyzed using a paired t-test or ANOVA.
D. A chi-square test is not suitable for assessing whether the prevalence of a specific gene is equal in two populations. This hypothesis involves comparing the gene frequencies between two groups, which requires calculating the Fisher's exact test or the Mantel-Haenszel test, depending on whether the populations are independent or not.
**Core Concept:** Chi-square test is a statistical tool used to determine whether there is an association between two categorical variables.
**Why the Correct Answer is Right:** The correct answer, hypothesis C, involves testing whether the distribution of a particular disease is independent of gender. This means assessing whether the disease prevalence is the same in males and females. Chi-square test is appropriate for this hypothesis as it evaluates the association between two categorical variables (disease status and gender) by comparing observed and expected frequencies in a 2x2 contingency table.
**Why Each Wrong Option is Incorrect:**
A. The hypothesis involves comparing the age distribution between two groups, which is a continuous variable and should be analyzed using a paired t-test or ANOVA.
B. The chi-square test is designed to evaluate the relationship between categorical variables, but it is not suitable for assessing the difference in height between males and females, which is a continuous variable and should be analyzed using a paired t-test or ANOVA.
D. The hypothesis involves comparing gene frequencies between two populations, which requires Fisher's exact test or the Mantel-