Mathematics 243
Two populations
Day 26 - The Ides of March
Do left-handed people die earlier, on average, than right-handed people?
1. Give some reasons why left-handed people might have a shorter life expectancy than right-handed people.
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2. The Pythagorean rule of variances. If x and y are independent variables then σx+y
= σx2 + σy2 .
3. The sampling distribution of the difference of sample means.
Suppose that two populations are approximately normal with mean and standard deviations µ1 , σ1 , µ2 and σ2
respectively and that we choose simple random samples from each of size n1 and n2 respectively. Then the following
statistic has approximately a t-distribution (with a number of degrees of freedom that can be computed from n1 ,
n2 , s1 and s2 respectively)
(x̄1 − x̄2 ) − (µ1 − µ2 )
q 2
s22
s1
n1 + n2
4. Inference for the difference of the sample means using the t-test.
5. Dead baseball players.
> DeadBB=DeadBB[DeadBB$birthYear=='1934',]
> aggregate(age~bats,data=DeadBB,FUN=summary)
bats age.Min. age.1st Qu. age.Median age.Mean age.3rd Qu. age.Max.
1
L
46.0
52.0
63.0
60.8
71.0
72.0
2
R
39.0
62.5
64.0
63.8
71.0
73.0
> aggregate(age~bats,data=DeadBB,FUN=sd)
bats
age
1
L 11.519549
2
R 9.929753
> t.test(age~bats,data=DeadBB)
6. Discussion of studies.
Temperatures of Calvin students
The body temperatures of 130 students are in the normaltemp dataframe in the M241 package as is their gender.
1. Is there a statistically significant difference between the body temperature of Calvin males and Calvin females?
2. What assumptions do you need to make in order to perform this analysis and do you think the assumptions are
plausible in this case?
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