In testing $H _ { 0 } : \beta _ { 1 } = 0 \text { versus } H _ { \pm } : \beta _ { 1 } \neq 0$ using a sample of 22 observations, the test statistic value is found to be t = -2.528. the approximated P-value of the test is
A) .01
B) .02
C) .025
D) .05
E) .99

Question

Quizplus · Accepted Answer

The P-value in a two-tailed test is twice the area in one tail of the distribution. Given the test statistic t = -2.528 and assuming a t-distribution (since the sample size is relatively small and the population standard deviation is unknown), the area in one tail corresponding to t = -2.528 is approximately 0.01 (based on t-distribution tables or software). Therefore, the P-value for the two-tailed test is approximately 2 * 0.01 = 0.02.

In Testing H0:β1=0 versus H±:β1≠0H _ { 0 } : \beta _ { 1 } = 0 \text { versus } H _ { \pm } : \beta _ { 1 } \neq 0H0​:β1​=0 versus H±​:β1​=0

In Testing $H _ { 0 } : \beta _ { 1 } = 0 \text { versus } H _ { \pm } : \beta _ { 1 } \neq 0$