Exercise 4.2.14 let a ⊆ r, let f : a → r, and let c ∈ r be a cluster point of a. if limx→c f exists, and if |f| denotes the function defined for x ∈ a by |f|(x) : = |f(x)|, prove that limx→c |f| = limx→c f .

On a certain portion of an experiment, a statistical test result yielded a p-value of 0.21. what can you conclude? 2(0.21) = 0.42 < 0.5; the test is not statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant. 0.21 > 0.05; the test is statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time, so the test is not statistically significant. p = 1 - 0.21 = 0.79 > 0.05; the test is statistically significant.