Final answer:
To test if the slope in a simple regression is non-zero, a t-test is used to compare the sample regression coefficient against zero, and ANOVA is used to test the overall significance of the model, which includes testing that at least one predictor has a non-zero slope.
Step-by-step explanation:
To test whether the slope in a simple regression is non-zero, we typically use two methods: the t-test and ANOVA (Analysis of Variance). The t-test compares the sample regression coefficient to a theoretical distribution under the assumption that there is no relationship between the variables (meaning the slope should be zero). When we perform a regression analysis, we often include an F-test (part of ANOVA) to test if at least one of the predictors in the model has a non-zero slope, which tests the null hypothesis that all regression coefficients are zero against an alternative hypothesis that at least one is not.
In the context of the options provided, the correct answer would be B) T-Test and ANOVA. The t-test specifically assesses whether the slope coefficient for the predicted variable differs significantly from zero, while ANOVA can test the overall significance of a model that may have one or more predictors, assessing whether the group means are from populations with the same mean (in the context of regression, it translates to testing the overall fit of the model).