ttest:
1) A cognitive psychologist
designed an experiment to test the hypothesis that people 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 50 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 
Random
order 
40 
17 
35 
19 
25 
21 
33 
25 
39 
15 
21 
9 
42 
11 
37 
7 
36 
13 
40 
22 
29 
26 
31 
13 
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:
Old program
n=12 variance = 1.00 mean = 25.0

New program
n=13 variance = 1.5 mean = 27.0

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.

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

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 (not associated). What is your conclusion?
Answers:
1)
Calculated tvalue of t=6.77; critical value (Alpha=.05, df=22)=1.72.
Therefore, reject Ho. Participants in categorized groups (M=34) recalled
significantly more words than participants in random order group.
2) Calculated tvalue of
t=4.46 critical value (Alpha=.05, df=23)=1.71.
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'.