Null hypothesis / Z-test

#1
Hey all!
I have a problem I cant solve. We have to formulate and reject or not 3 null hypothesis. I could formulate them but I cant do the z-test. I didnt write the null hypotheses yet tho, all I need really are the results of the z-test.

Heres the instructions "In the results section: (1) present the means and standard deviations of the correct number of words recalled for each of the four groups. (2) To check whether the experimental hypotheses were supported, conduct 3 different Z-tests. State the three null hypotheses and report the values of your Z statistics. Make all the necessary group comparisons: Compare Group 1 with Group 2, Group 3 with Group 4, and Groups 1+3 with Groups 2+4. (All hypotheses are tested at alpha = 0.05, where Z = ±1.96)."

The data show 52 people who had to remember words and the Yes/No show how much words were remembered by the 14 men and women and the Letter E shows how much E men and women counted in some words.

Men Yes/No Men Letter E Women Yes/No Women Letter E

4 - 4 - 5 - 6
8 - 6 - 11 - 4
5 - 6 - 14 - 1
14 - 6 - 9 - 0
11 - 3 - 11 - 4
6 - 0 - 10 - 4
9 - 4 - 10 - 3
9 - 8 - 7 - 2
10 - 2 - 9 - 6
8 - 3 - 9 - 5
12 - 4 - 11 4
11 - 5 - 7 - 3
8 - 2 - 12 - 5
4 - 2 - 7 - 1
(The data are in 4 colums, but the forums dont show all the spaces so you have to understand that the first number is Men Yes/No, the second Men E, etc. Theres no negative, the - is just to separate)
______________________________________________________
mean 8.5 3.92 9.42 3.42
SD: -2.43 -3.29 -2.21 -3.37
SE: -0.66 -0.87 -0.59 -0.9 (standard Error)
V 5.90 10.82 4.88 11.35 (Variance)

Under the line is what I found, and those are all the datas we have. We dont have the SD of the population, the mean of the population or anything else.

Any help to do the z test would be VERY apreciated! What I really need is the population or null hyp mean, I really dont know how to get it.
Thanks in advance for all responses!

pr1nce
 
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Mean Joe

TS Contributor
#2
Check that I'm understanding the data above correctly: the first (left-most) column is Group 1? And Group 2 is the third (second from the right) column? It seems that would be the logical thing to test: the # of words remembered by men (first column) vs # of words remembered by women (third column).

Going by that assumption...

Test 1: Comparing Group 1 with Group 2
Let M1 = true average number of words remembered by men
Let M2 = true average number of words remembered by women

Null hypothesis: M1 = M2 (equivalently, M1-M2 = 0, this is how you get your null hypothesis mean)

Test statistic:
Let X1 = sample average number of words remembered by men
Let X2 = sample average number of words remembered by women

z = [0 - (X1 - X2)] / pooled sample standard error
This is a two-sided test, so the sign of z doesn't matter (i.e. it doesn't matter if X1 is for men, or if you want X1 for women)
You know how to find pooled standard deviation?

The data show 52 people who had to remember words and the Yes/No show how much words were remembered by the 14 men and women and the Letter E shows how much E men and women counted in some words.
This is probably just a small thing, but I'm not understanding the count of 52 people..there were 14 men + 14 women = 28?
 
#3
Mean Joe you rock. The only Thing I was missing was the 0.

The 52 is actually a 56 sorry about that, or 28 it doesnt really matter. When the teacher explained it he said it were different people in the Men Yes/No and in the Men letter E.

Really the only thing I didnt get was the d in the forumla ((X1-X2)-d) / SE that I got from Statistics Tutorials website (stattrek.com)

Does it matter tho if the d (0) is before the formula or after the formula? Cause on Statistics tutorials it says after and you said before. Ill do both cal anyways, maybe it gives the same thing.

What I still dont understand is why did he ask us to compare the First and second columns as they dont analyse the same datas.

Anyways Ima get to work on this right now.
Thx Mean Joe

BTW Mean Joe, or anybody else, how would you write the null hypothesis from Men Yes/No and Women Yes/No, (written formulated hypothesis) cause Im not sure that I could formulate well.
 

Mean Joe

TS Contributor
#4
Really the only thing I didnt get was the d in the forumla ((X1-X2)-d) / SE that I got from Statistics Tutorials website (stattrek.com)

Does it matter tho if the d (0) is before the formula or after the formula? Cause on Statistics tutorials it says after and you said before. Ill do both cal anyways, maybe it gives the same thing.
The sign of the test statistic will change (positive to negative), but the conclusion of the test should not. Because you are doing a two-tailed test, so you will compare the absolute value of the test statistic to 1.96 (for alpha=.05 level)

What I still dont understand is why did he ask us to compare the First and second columns as they dont analyse the same datas.

Anyways Ima get to work on this right now.
Thx Mean Joe

BTW Mean Joe, or anybody else, how would you write the null hypothesis from Men Yes/No and Women Yes/No, (written formulated hypothesis) cause Im not sure that I could formulate well.
I don't understand the data either, so can't figure out the null hypothesis. I thought that first column was # of words remembered by men. It's "Men Yes/No" instead--whatever that's supposed to mean?
 
#5
I think its like they asked people if they remembered wors and they had to say Yes or No. I dont know he didnt explain so I have no clue how to formulate this hypothesis :(

**** I guess Ill just risk something.I really have no clue.

And I figured the first two null hypothesis would be for comparing group 1 &3 (assuming that group 1 is column 1 and group 3 colum 3)
Then the secnd null can be 2 & 4 because they analyse the same datas, but what would or could be the third null hypothesis?

If its 1 & 2 (even tho one counts the Yes/No and two the Letter E, and it doesnt make any sense to compare them) why not four hypothesis? I really dont undertsand this. Im starting to believe the teacher gave an assignment with incomplete data. Maybe he gave some in class and didnt put it on the sheet, but that would be rather unusual and pretty pointless since thats why you ahev an assignment sheet. If he did that, I wasnt there on that class and missed some info. That would explain my questions lol.

And lat thing lol. If its between +1.96 and -1.96 its not rejected right? and greater or smaller than those two is rejected? Did I AT LEAST got this part right? lol
 
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