Which statement best defines the population slope beta and explains why beta = 0 indicates no linear correlation?

From a LinRegTTest you obtain sample slope b = 0.40, standard error SE_b = 0.12, and n = 20. Using a two-sided test at alpha = 0.05, compute the t statistic, approximate p-value, and state the decision.

Which TI-84 input entries are required to construct a 95% confidence interval for the population slope using LinRegTInt when hours are in L1 and scores in L2?

Using the relationship between correlation r and the t statistic for testing beta = 0 (t = r * sqrt((n-2)/(1-r^2))), compute the t statistic and two-sided p-value approximation for r = 0.45 and n = 22. State the conclusion at alpha = 0.05.

A dataset of 9 observations shows a strong sample slope but a residual plot reveals a curved pattern. Evaluate whether t-based inference about beta is appropriate and justify your recommendation.