Q.100 - The Practice of Statistics for AP

Question

You are testing $H_O:\mu =10$$H_{\alpha }:\mu <10$ against  based on an SRS of $20$ observations from a Normal population. The $t$ statistic is . $t=-2.25$The $P$-value

(a) falls between $0.01 and 0.02$

(b) falls between$0.02 and 0.04$

(c) falls between$0.04 and 0.05$

(d) falls between $.05 and 0.25$.

(c) is greater than$0.25$.

Step-by-Step Solution

Answer

(a) The $P$- value falls between $0.01 and 0.02$.

Step-1 Given Information

Given In the question that,

The null and alternative hypothesis are:$H_0:\mu =10$

                                                                   $H_{\alpha }:\mu <10$

Test statistic($t$)$=-2.25$

Sample size $\left(n\right)=20$ we have to find the correct option.

                                                                  

Step-2 Explanation

Degree of freedom can be calculated as:

         $df=n-1$

             $=20-1$

             $=19$

The $p$ value is $0.01<p<0.02$

Thus the correct option is (a)