Suppose a hypothesis test is performed to determine if the variable MASS is helpful in explaining metabolic rate after accounting for the effects of sex. What is the correct test-s... Suppose a hypothesis test is performed to determine if the variable MASS is helpful in explaining metabolic rate after accounting for the effects of sex. What is the correct test-statistic to use?
Understand the Problem
The question is asking about which test statistic, either t-statistic or F-statistic, is appropriate to use in a hypothesis test concerning the relationship between mass and metabolic rate while accounting for sex.
Answer
The correct test statistic to use is the F-statistic.
Answer for screen readers
The correct test statistic to use is the F-statistic.
Steps to Solve
- Identify the type of test being conducted
In this scenario, the goal is to determine if the variable MASS is significant in explaining the metabolic rate while accounting for the variable SEX. This situation indicates a multiple regression analysis.
- Recognizing the appropriate test statistic
For hypothesis tests in multiple regression, the F-statistic is used. It helps assess the overall significance of the regression model, particularly when multiple predictors (like MASS and SEX) are involved.
- Understand the analysis of variance output
The provided output includes an Analysis of Variance (ANOVA) table. The F-statistic in this table (31.90) assesses whether the model with both predictors fits significantly better than a model without them.
- Conclusion on test-statistic use
Given that we're using multiple predictors and examining the overall model significance, the correct test statistic to use in this hypothesis test is the F-statistic.
The correct test statistic to use is the F-statistic.
More Information
The F-statistic evaluates the ratio of variance explained by the model to the variance not explained, helping determine if at least one predictor (like MASS) adds significant information to the model.
Tips
- Confusing the t-statistic with the F-statistic; the t-statistic is typically used for hypothesis tests concerning individual regression coefficients while the F-statistic evaluates the overall model fit.
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