APFIVE After carrying out both a hypothesis test and constructing a confidence interval for the slope, rank the following conclusions in order of strength of evidence supporting a linear relationship in the data, from strongest to weakest: (a) The hypothesis test yielded a p-value much less than 0.05, (b) The 95% confidence interval for the slope does not include 0, © The t statistic is large in magnitude, and (d) The coefficient of determination (R²) indicates that a substantial proportion of the variability in $$y$$ is explained by $$x$$.
| Conclusion Component | Interpretation |
|---|---|
| (a) Hypothesis test with p-value < 0.05 | Strong statistical evidence against \(H_0\) |
| (b) 95% confidence interval not containing 0 | Interval suggests a nonzero slope |
| © A large magnitude t statistic | Indicates a substantial signal relative to variability |
| (d) A high coefficient of determination (R²) | Suggests that a significant portion of variability is explained by the model |
The t statistic is large in magnitude, The hypothesis test yielded a p-value much less than 0.05, The 95% confidence interval for the slope does not include 0, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
The hypothesis test yielded a p-value much less than 0.05, The 95% confidence interval for the slope does not include 0, The t statistic is large in magnitude, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x, The t statistic is large in magnitude, The 95% confidence interval for the slope does not include 0, The hypothesis test yielded a p-value much less than 0.05
The 95% confidence interval for the slope does not include 0, The hypothesis test yielded a p-value much less than 0.05, The t statistic is large in magnitude, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
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