Q.101 - The Practice of Statistics for AP

Question

You are testing $H_0:\mu =10$ against $H_{\alpha }:\mu \ne 10$ based on an SRS of $15$$t$ observations from a Normal population. What values of the   statistic are statistically significant at the$\alpha =0.005$ level?

(a) $t>3.326$

(b) $t>3.286$

(c) $t>2.977$

(d) $t<-3.326 or t>3.326$

(c) $t<-3.286 or t>3.286$

Step-by-Step Solution

Answer

The values of the   statistic are statistically significant at the $\alpha =0.005$ level is (d)$t<-3.325 or t>3.326$

Step 1: Given Information

Given in the question that,

$H_0:\mu =10$

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

$n=15$

$\alpha =0.005$ we have to find the correct option.

Step 2: Explanation

Identifying the important values in the row with the degree of freedom

 $df=n-1$

     $=15-1$

     $=14$

 and in the column with$\alpha /2=0.005/2$

                                               $=0.0025$

in table B :

$t=\pm 3.326$

The test is then statistically significance for values more extreme than the critical values and therefore it is $t<-3.326 or t>3.326$