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) $t<-3.326ort>3.326$

(c)$t<-3.286ort>3.286$

Short answer

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

Step-by-step solution

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 $t<-3.326ort>3.326$