The sign test is a non-parametric test that evaluates whether the observed number of positive differences significantly deviates from the expected number under the null hypothesis. For a sample size of 100 trading days, the null hypothesis assumes that the probability of a positive or negative differential is 0.5. You can calculate the critical values using the binomial distribution or its normal approximation (suitable for large sample sizes, such as 100 days).

A is incorrect: While chi-squared tests are used in statistical analysis, they are primarily for testing relationships between categorical variables or goodness-of-fit. The sign test, however, relies on the binomial distribution (or its normal approximation) to evaluate whether the observed number of positive differences significantly deviates from the expected value.

B is incorrect: While likelihood ratio tests are widely used to compare model fits, they are not applicable to the sign test, which focuses on the directional frequency of differences rather than fitting models to observed data. This distractor is plausible because likelihood ratio tests are common in model comparison contexts.

D is incorrect: While calculating proportions may seem logical, the sign test evaluates the number of positive differences, not proportions. The proportion might suggest the result but is not the formal statistical step required to assess significance.