Final answer:
In a statistical test, variables with t-values less than the critical t-value, based on the degrees of freedom and significance level, are those that may be dropped as they do not contribute significantly to the model.
Step-by-step explanation:
When deciding which variables can be dropped based on their t-values, you look for variables with t-values that are not significant. For a two-tailed test with a given level of significance (commonly α = 0.05), you compare the absolute value of the t-value for each variable to the critical t-value from the t-distribution for your degrees of freedom. If the absolute t-value is less than the critical value, there is insufficient evidence to conclude that the variable contributes significantly to the model, and thus the variable may be dropped from the model. For instance, if you have 29 degrees of freedom and a significance level of α = 0.05, the critical t-value is 2.045. A t-value less than 2.045 would suggest that the variable is not significantly different from zero.
In the options presented, variables with a t-value less than 1.96 could be considered for dropping from the analysis, assuming a significance level of α = 0.05 and a sufficient degree of freedom. However, a t-value of 1.96 may not always be the appropriate critical value, as critical t-values change with the number of degrees of freedom. Thus, it is important to always check the correct critical value for the specific test being conducted.
When applying this to an actual test, if a variable's t-value is less than the critical t-value from a Student's t-distribution appropriate for the sample size and desired confidence level, you would typically fail to reject the null hypothesis and consider the variable as providing no evidence of significant correlation in the data.