William H. Knapp III

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This homework was due on Friday, November 16 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. What test should you use to test the hypothesis that a mean is equal to some value when you don't know the population variance.
Independent t-test.
One-sample t-test.
Paired t-test.

2. What type of test should you use if you have two correlated samples and don't know the population variance.
Independent t-test.
One-sample t-test.
Paired t-test.

3. What happens when you add two independent sets of scores together?
The variance of the sum is greater than the variance of either of the individual sets.
The variance of the sum is less than the variance of the individual sets.
The variance of the sum is the same as the variance of the more variable set.
There is not enough information to tell.

4. What happens when you subtract one set of scores from another?
The shared variance of the sets add.
The shared variance of the sets is eliminated.
The shared variance of the sets adds for paired samples and subtracts for independent samples.
There is not enough information to tell.

5. When is a paired t-test preferred over an independent t-test?
Any time the samples are paired.
Any time the samples are paired on some variable(s) that affect the variable of interest.
Any time the samples are paired on some variable(s) that affect the variable of interest other than the variable of interest itself.
All the time.

6. Compared to two-tailed independent t-tests, what variables should be smaller for corresponding paired t-tests when the samples have been paired appropriately?
The critical values for t.
The observed t-statistic.
The p-value.
The standard error term.

7. Imagine you performed a paired t-test with an alpha level .01. There were 25 observations in each sample and the observed t-statistic was 7.3. How should you report your results in APA format?
p<.01, t(7.3)=50
p>.01, t(48)=7.3
t(24)=7.3, p<.01
t(48)=7.3, p>.01
t(7.3)=24, p=.01

8. For the next set of questions, please download this data save it and load it appropriately into R.
If a question requires you to create a difference score, please subtract the sample 2 data from the sample 1 data to ensure we get the same answer.
Imagine you're offering statistical consultation and analysis services while you're in college so you have extra spending money. A frantic psychologist runs up to you and gives you the data for sample 2. He wants it analyzed and tells you to use an alpha of .01. After questioning, you discover that he's interested in whether or not frequent facebook users are unhappier than average. Not knowing what 'average' means, you question him further and discover that he's given a sample of frequent facebook users a happiness test with a mean of 100 where higher scores indicate more happiness. Armed with this information, you begin your work. What's the critical t for the test you should perform?

9. What's the standard error term that you'll use for your test?

10. What's the observed value of t?

11. What should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

12. What's the p-value for the test you performed?

13. Still glowing with pride from the fact that you completed the task so quickly in R, you call the professor to come pick up the results. The professor stops by and looks angrily at your work. "Humph! You shouldn't have done a one tailed test." Based on what they told you before, you knew you did the right thing originally. Since you need the money, you decide not to tell this absent-minded professor off. Like a honey badger grabbing a king cobra, you grab the results and quickly update the p-value. Astonished the professor hands you your money. What's the new p-value?

14. The next day, the professor accosts you and even more frantically tells you that they forgot to give you the data for the sample 1 control group of infrequent facebook users. "No problem," you say. You take a quick look at the data and notice they look strongly correlated. You ask, "These are paired samples right?" The frenetic professor looks quizzically for a moment before telling you the samples are independent. When you ask if they're sure, the professor huffs off shouting "Of course I'm sure. I'm the professor here! Make sure you use a two-tailed test with an alpha level of .01." What's your new standard error term?

15. What's the corresponding t-statistic?

16. What's the corresponding p-value?

17. Just as you're getting ready to call the professor, they burst in on you. Like a maniac they're shouting "Of course the samples were paired, stupid. I was testing you and you failed. Now redo the analyses correctly." Having had enough, you tell the professor that if they want you to help them any more, they're going to have to pay you twice as much, up-front, and in cash. The professor hangs their head and says "Ok, what else can I do. I wish I would have studied statistics harder when I was a student." You tell them to grab a chair and some tea while you redo the analyses. What's the new standard error term?

18. What's the corresponding t-statistic?

19. What's the corresponding p-value?

20. What does this evidence suggest?
Frequent facebook users are happier.
Frequent facebook users are less happy.
Frequent facebook users are equally happy.
We need more information before we can draw a conclusion from these data.