2) Two individuals are running for mayor of Tallahassee. You conduct an election survey
(N = 561) a week before the election and find that 57% of the respondents prefer
candidate A. Can you predict the winner (α = 0.01)? (Hint: Use 50% as the proportion
of votes needed for a tie in a two-candidate race). [15 points]
3) A random sample of 97 Chinese Americans has finished an average of 13.5 years of
formal education with a standard deviation of 1.7 years of formal training. The national
average is 12.4 years. State a null and alternative hypothesis regarding a possible
difference in years of formal education between Chinese Americans and the whole
population? Can you reject your null hypothesis for α=0.05 (two-tailed)? [10 points]
4) The overall proportion of turnout in the previous elections was 0.43. You took a
random sample of size N =150 from a neighborhood with relatively wealthy and well
educated people. The sample proportion of voter turnout is = 0.51 S P .
a) State a null hypothesis and alternative hypothesis regarding a possible difference in
voter turnout between your sample and the whole population. [5 points]
b) Test your hypotheses (α=0.05, two-tailed). Can you reject your null hypothesis? Does
your decision change when you use α=0.01 (two-tailed) instead? [10 points]
c) Based on your research results from the first sample, you decide to take another sample
from a neighborhood with relatively poor and less educated people. The sample size is
177 2 N = and the sample proportion of voter turnout is 0.37 2 = S P . Can both samples be
treated as representatives of the same population? State a null hypothesis and alternatives
hypothesis and make a statistical test (two-tailed, for both α=0.05 and α=0.01). [15
points]
5) For 2006, a sample of SAT scores of = 1,751 female N female freshmen has mean scores
of female, verbal = 493.7
S μ for the verbal subtest and female, math = 501.2
S μ
for the math subtest,
with standard deviations s female, verbal = 99 and s female, math =111, respectively. Moreover,
the mean scores of a sample of = 2,577 male N male freshmen are male, verbal = 503.9
S μ
for
the verbal subtest and male, math = 542.9
S μ
for the math subtest, with standard deviations
smale, verbal =115 and smale, math = 95, respectively.
a) State a null hypothesis and alternative hypothesis about possible differences in scores
between the female and male samples for the verbal subtest, make a statistical test (use
α = 0.05, two-tailed) and, finally, make your decision between both hypotheses.
[15 points]
b) Do the same thing as in a), but now for the math subtest