Child Development 250 (01) - Research Methods 
Spring, 2010 (Hembree)

Practice Problems

 

T-test:

1) A cognitive psychologist designed an experiment to test the hypothesis that children remember words better when the words are categorized. She randomly assigned participants to one of two groups (categorized or random order), then presented the same 10 words in either a categorized (animals, food, colors) or random order.  After the words were presented, the researcher asked participants to recall as many words as possible, producing the following results:

 

Categorized (n=11) Random order (n=11)
9 8
10 7
8 6
7 6
7 5
8 5
9 5
9 6
8 6
7 7
6 5

Conduct a t-test to determine whether participants for whom the words were categorized recalled more words than participants for whom the words were random.

2) An educational psychologist wants to compare children's math scores as a function of their participation in a new math curriculum. She randomly assigns the children to either the usual curriculum or the new curriculum, then measures math performance on a standardized test. She obtains the following results from both groups:

Old program (n=10) New program (n=9)
1 4
4 5
3 5
5 6
2 2
3 7
5 6
6 9
2 5
4

Conduct a t-test to determine whether the children's test scores were better with the new curriculum.

 

Chi-square:

3) The relationship between smoking and cause of death was studied for a sample of people who recently died.  The deceased were classified as smokers or nonsmokers and their cause of death classified as either cancer or other causes.

 

Smoker?

Cause of death Yes  No
Cancer 46 25
All other causes 34 45

Conduct a Chi-square test to determine whether smoking is related to cause of death.

 

4) A bond issue is to be put before the voters in a forthcoming election. An opinion poll company obtains a random sample of 200 registered voters and asks them what party they belong to and how they intend to vote on the issue.  The results are as follows:

 

 

Prospective vote on bond issue

Political party Yes No undecided
Democratic 20 30 10
Republican 30 30 20
Other 10 40 10

Test the null hypothesis that political party and prospective vote on the bond issue are independent.  What is your conclusion?

Pearson r

5) An educational psychologist wants to test whether hours spent doing math homework is related to math test performance. She recruits 4th grade students and their families to participate in the study. She measures hours spent doing math homework by asking the families to report the number of hours spent in the week before a math quiz,  then obtains the students' math test scores. Compute a Pearson r to test the association between homework and math scores. 

Hours in homework test scores
5 5
10 20
6 4
8 15
4 11
4 9
3 12
10 18
2 7
6 2
7 14
9 17

  

Answers:

1) Calculated t-value of t=4.28; critical value (alpha=.05, df=20, two-tailed) = 2.09. Therefore, reject Ho. Participants in categorized groups recalled significantly more words than participants in random order group.

2) Calculated t-value of t= -2.40; critical value (alpha=.05, df=17, two tailed)=2.11. Therefore, reject Ho. Children's math scores were significantly better with the new curriculum.

3) χ2= 7.11 

df=1; critical value = 3.84

Reject Ho. There is a significant association between smoking and cause of death. Smokers are more likely to die of cancer than non-smokers.

4) χ2= 12.77

df=4; critical value = 9.49

Reject Ho.  There is a significant association between political party and prospective vote. Republicans are less likely to vote 'no' and those describing themselves as 'other' are more likely to vote 'no'.

5) r=.667; critical value (alpha=.05, df=10) = .576 

Reject Ho. The two scores are significantly positively correlated. 

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Send problems, comments or suggestions to: hembrees@csus.edu. Updated: January 15, 2010

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