

Practice Problems 

Ttest: 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:
Conduct a ttest 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:
Conduct a ttest to determine whether the children's test scores were better with the new curriculum.
Chisquare: 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.
Conduct a Chisquare 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:
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.
Answers: 1) Calculated tvalue of t=4.28; critical value (alpha=.05, df=20, twotailed) = 2.09. Therefore, reject Ho. Participants in categorized groups recalled significantly more words than participants in random order group. 2) Calculated tvalue 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) χ^{2= }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 nonsmokers. 4) χ^{2= }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.



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