Find the $P$-value for the given test statistic $t$, sample size $n$, and alternate hypothesis $H _ { 1 }$. $t = 1.726 , n = 22 , H _ { 1 } : \mu \mu _ { 0 }$ A) 0.25

Question

Find the $P$-value for the given test statistic $t$, sample size $n$, and alternate hypothesis $H _ { 1 }$.
$t = 1.726 , n = 22 , H _ { 1 } : \mu > \mu _ { 0 }$
A) 0.25 < P < 0.4
B) 0.05 < P < 0.1
C) 0.025 < P < 0.05
D) 0.01 < P < 0.025

Quizplus · Accepted Answer

To find the $P$-value in this case, we need to find the area to the right of the test statistic ($t = 1.726$) under the $t$-distribution with $n-1$ degrees of freedom. Using a table or calculator, we find that the area to the right of $t=1.726$ with $21$ degrees of freedom is approximately $0.049$.

Since the alternative hypothesis is $H_1: \mu > \mu_0$, we are interested in the area to the right of the test statistic. Thus, the $P$-value is approximately $0.049$, which falls between 0.025 and 0.05. Therefore, the best choice is C.

Find The PPP -Value for the Given Test Statistic ttt , Sample Size

Find The $P$ -Value for the Given Test Statistic $t$ , Sample Size