I don't actually know anything about Cohen's D so I'm no help on problem 1.
You're doing way too much work here. I'm guessing you're used to doing your tests using a critical value. I'm not a fan of that approach. The approach I take and tend to see used more often is based on the p-value. You can determine whether you reject or fail to reject the null based on a p-value. In this question they give you the p-value (or at least a range for the p-value) so you don't need to worry about whether it's one sided or two sided or what the critical value is. They didn't even need to tell you what type of test it was, what the t-value was, or the degrees of freedom. Essentially this question boils down to "Your p-value is greater than .05: Do you reject or fail to reject the null hypothesis?"3. a research report describing the results from a REPEATED MEASURES T TEST states, "t(22)=1.71, p>.05". From this report you can conclude that the outcome of the hypothesis test was...
a. to reject the null hypothesis with a sample of n=23 participants
b. fail to reject the null hypothesis with a sample of n=23 participants
With this question, since it is a repeated measures exam, the df=n-1. Thus, 22+1 = 23 number of participants. I am confused about this question because I am unsure if its asking for a two tailed or one tailed. if t=1.71, and alpha is .05, and if it is one tailed, 1.717 is the critical region, thus rejecting the null hypothesis. However if it is a two tailed test, the critical region would be 2.074, thus fail the reject the null hypothesis. I dont understand how to observe if it is a one tailed test to look for for the critical region or a two tailed test.
I'm a little confused on this as well. If the samples had the same mean and variance it doesn't matter what the sample size was because you won't reject the null anyways. My guess is that they were trying to say that before the treatment was given the quantity of interest had the same sample mean and variance in both samples. If the treatment actually does have an effect will you be more likely to reject the null with a larger sample size or a smaller sample size.4. True or False, two samples are selected from a population and a treatment is administered to the samples. If both samples have the same mean and the same variance, you are more likely to find a significant treatment effect with a sample of n=100 than with a sample of n=4.
This is also a releated measures design where where two samples are selected from a population. I think that if you were to find out the significant effect it would be to calculate cohen's D. However, I am unsure with the way this question is worded. I do know that the reduction in the effect size, increases the sample variance. (but in the question it states the variances are the same). I am confused. =\