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 $0.01and0.02$

(b) falls between$0.02and0.04$

(c) falls between$0.04and0.05$

(d) falls between $.05and0.25$.

(c) is greater than$0.25$.

Short answer

(a) The $P$- value falls between $0.01and0.02$.

Step-by-step solution

Step-1 Given Information 

Given In the question that,

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

localid="1649247803052" $H_{\alpha }:\mu <10$

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)