please help I have thought through these questions but still am not certain

#1
1. two samples from the same population both have M=84 and s^2=20, however one sample has n=10 and the other has n=20 scores. Both samples are used to evaluate a hypothesis that μ=80 and to compute Cohen's d. How will the outcomes for the two samples compare?

a. the larger sample is more likely to reject the hypothesis and will produce a larger value for cohen's d

b. the larger sample is more likely to reject the hypothesis but the two samples will have the same value for cohen's d

c. the larger sample is less likely to reject the hypothesis and will produce a larger value for cohen's d

d. the larger sample is less likely to reject the hypothesis but the two samples will have the same value for cohen's d.

With this question, I read in my book that having a larger sample is more likely to reject the hypothesis. I believe that the answer is B because the values given are the same, thus the samples for Cohen's D would also be the same for the two samples. If the samples are from the sample population, then it would be a repeated measures design, thus the Cohen's D shouold be calculated Md/S. However I am not certain if this is the answer since in the question they gave M, and not Md.


2. in an independent measures hypothesis test, what must be true if t=0?
a. the two population means must be equal
b. the two sample means must be equal
c. the two sample variances must be equal
d. none of the choices are correct

With this question, I believe that none of the choices are correct, however whenever an answer is none of the above, I feel that it could be a trick question. I do know that in order for t to be closer to 0, the mean difference should be =0 since the formula for t is (M1-M2)-(mu1-mu2) / (s(m1-m2)

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.


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. =\

Please help! If possible could you guys please shows the steps on how the answers are achieved? thank you so much in advance![/QUOTE]
 

Dason

Ambassador to the humans
#2
I don't actually know anything about Cohen's D so I'm no help on problem 1.
2. in an independent measures hypothesis test, what must be true if t=0?
a. the two population means must be equal
b. the two sample means must be equal
c. the two sample variances must be equal
d. none of the choices are correct

With this question, I believe that none of the choices are correct, however whenever an answer is none of the above, I feel that it could be a trick question. I do know that in order for t to be closer to 0, the mean difference should be =0 since the formula for t is (M1-M2)-(mu1-mu2) / (s(m1-m2)
Let me ask you a question. You say that 'for t to be closer to 0, the mean difference should be = 0' which is true because when the mean difference is 0 what is t? Plug it in. You're testing for a difference in means so under the null mu1-mu2 = 0. So if M1-M2 = 0 what does t end up being?

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.
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?"

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. =\
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.
 
#3
Thanks for your help. I understand number 2 and 3 better now. However I am still confused with number 4 and still not sure about number 1. Anyone else want try explaining this to me? please?

I really appreciate your time and effort.

:yup: