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

`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.

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.