Question

A researcher obtains t = 2.35 for a repeated-measures study using a sample of n = 8 participants. Based on this t value, what is the correct decision for a two-tailed test?​

Answer 1

Answer:

$p_v =2*P(t_{7}>2.35)=2*0.0255=0.051$  

If we compare the p value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% or 1% of significance we fail to reject the null hypothesis.

Step-by-step explanation:

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level is not provided but we can assume it as $\alpha=0.05$. First we need to calculate the degrees of freedom like this:

$df=n-1=8-1=7$

The next step would be calculate the p value for this test.  Since is a bilateral test or two tailed test, the p value would be:  

$p_v =2*P(t_{7}>2.35)=2*0.0255=0.051$  

If we compare the p value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% or 1% of significance we fail to reject the null hypothesis.