Suppose that a t test of $H _ { o } : \mu = 250 \text { versus } H _ { \pm } : \mu \neq 250$ is based on 12 degrees of freedom. If the calculated value of the test statistic is 2.8, then the P-value is
A) .008
B) .992
C) .016
D) .492
E) .496

Question

Quizplus · Accepted Answer

The P-value for a two-tailed t-test is found by doubling the area in one tail beyond the test statistic. Since the test statistic is 2.8 and the degrees of freedom are 12, we look up the area in the t-distribution table for a t-value of 2.8 with 12 degrees of freedom. This area represents the probability of observing a value as extreme or more extreme than our test statistic under the null hypothesis. Since tables might not give an exact value for 2.8, we know the P-value is the area in both tails combined. Given the choices, the correct P-value must be small, reflecting the unlikelihood of observing such a test statistic under the null hypothesis. Choice C (.016) is the correct P-value, as it represents a small probability consistent with a significant result at common alpha levels (e.g., 0.05, 0.01), indicating that the test statistic of 2.8 is significantly different from the null hypothesis value of 0 at a level of significance that would typically lead to rejection of the null hypothesis. This is because the P-value is essentially the probability of observing a test statistic as extreme as or more extreme than the one calculated (2.8) if the null hypothesis were true.

Suppose That a T Test Of Ho:μ=250 versus H±:μ≠250H _ { o } : \mu = 250 \text { versus } H _ { \pm } : \mu \neq 250Ho​:μ=250 versus H±​:μ=250

Suppose That a T Test Of $H _ { o } : \mu = 250 \text { versus } H _ { \pm } : \mu \neq 250$