At the .05 significance level, the null hypothesis $H _ { o } : \mu _ { D } \geq 0$ is rejected in a paired t test, where the data consists of 15 independent pairs, if A) $t 1.761$ C) either $t \langle - 1.761 \text { or } t 1.761$ D) $t 1.701$

Question

At the .05 significance level, the null hypothesis $H _ { o } : \mu _ { D } \geq 0$ is rejected in a paired t test, where the data consists of 15 independent pairs, if A) $t < - 1.761$ B) $t > 1.761$ C) either $t \langle - 1.761 \text { or } t > 1.761$ D) $t < - 1.701$ E) $t > 1.701$

Quizplus · Accepted Answer

For a paired t-test with a null hypothesis $H_0: \mu_D \geq 0$, rejecting the null hypothesis at the .05 significance level (two-tailed) involves looking at the critical t-value for a given degrees of freedom (df). Since we have 15 pairs, the degrees of freedom is $15 - 1 = 14$. The critical t-value for a two-tailed test at the .05 level for 14 degrees of freedom is approximately ±2.145 (depending on the t-distribution table used). However, given the options, the closest and applicable critical value for a one-tailed test (since the hypothesis is directional with $\geq$) is -1.761, indicating that for values of t less than -1.761, the null hypothesis would be rejected. This suggests a misunderstanding in the framing of the question or the provided options, as they seem to imply a one-tailed test scenario. Nonetheless, based on the given options, A is the correct choice for rejecting the null hypothesis in a scenario that seems to be interpreted as a one-tailed test.

At the 05 Significance Level, the Null Hypothesis Ho:μD≥0H _ { o } : \mu _ { D } \geq 0Ho​:μD​≥0

At the 05 Significance Level, the Null Hypothesis $H _ { o } : \mu _ { D } \geq 0$