1. Regression (Ch. 5):
Here are the data of average time spent reading per day per perso n and the
rates of Alzheime r’s disease for 5 unna me d coun tries.
reading time (minutes)
26 30 34 27 15
Alzh. rate (# deaths per 100,000 people) 1.9 1.7 1.5 1.7 2.3
The correlation between reading times and death rates in this data set is
r= - 0.98
We would like to know whether rate of death from Alzheime r’s can be predicte d
from the average reading time.
a) Find the mean reading time and the mean Alzheimer’s rates in this data set.
b) Find the standa r d deviation of both reading times and death rates
c) Make a scatter plot (Hint: think about which variable to put on the horizo n t al
axis)
d) Find the equation for the regression line
e) Plot the regression line on the same grap h as the scatte r plo t
f) Based on your results, what Alzheime r’s death rate would you predict for a
country with average reading time 20 minu te s per day per perso n?
2. Quality of data (Ch. 7, 8)
In order to asses s the opinion of stude n t s at the U on camp u s safety, a reporte r
interviews 15 stude nt s he meets walking on the camp u s late at night who are
willing to give their opinion.
a) Is this an experime n t or an observation al study?
b) What is the population that the reporte r is trying to study?
c) What is the sample?
d) Do you think this is a good way to obtain the data for this study? Why or why
not?
3. Probabilities: (Ch. 9, 11 )
Inhabitan t s of a planet M can be red, blue or green and have 2, 3 or 4 legs. Here
are the distributions:
color
red blue green
portion of population 0.4 0.5
0.1
# of legs
Portion of popula tio n
2 3 4
0.1 0.8 0.1
a) What is the probability that a rando m ly chosen inhabita n t is either red or
green?
b) What is the probability that a rando mly chosen inhabitan t has more legs than
you do?
c) A study shows that not only P(red)= 0.4, and P(3 legs)=0.8, but also the
probability that an inhabitant is red and has 3 legs is 0.3. Make a Venn diagra m
to reflect these data.
d) What is the probability that a rando m ly chosen inhabitan t has 3 legs, but
isn’t red?
e) What is the probability that a rando mly chosen inhabita n t neither has 3 legs
nor is red?
f) Are the events of being red and having 3 legs indepen d e n t? (Hint: use
multiplication rule for indepe n d e n t events)
4. Distribution of xbar (Ch. 10) (also involves Normal comp u t a tio n s, ch. 3):
Newborn babies have mean weight μ = 3200 g and the stan d ar d deviation σ =
470 g. There are 100 babies born in the hospital on a particular week, and the
hospital repor t s their average weight to a newspa pe r.
a) What is the distribution of the mean weight of these 100 babies?
b) What is the probability that the reporte d weight is below 3100 g?
c) What is the probability that the reporte d weight is between 3100 and 3250 g?
d) What is the weight level such that the probability for the reporte d weight
to be above that level is 0.05?
5. Basics of confide nce intervals (Ch. 13)
You measur e the weights of a ran do m sample of 25 male runne r s. The sample
mean is 60 kilogra m s (kg). Suppos e that the mean weights of male run ners
follow a Normal distribu tion with unknown mean µ and stan da r d deviatio n
σ = 5 kg.
a) Find a 95% confidence interval for µ.
b) Explain in words what the confidence interval from part a) means.
c) Suppose that I compu te a 98% confide nce interval. Withou t actually
compu ti ng this new interval yourself, say whether it would be larger or
smaller than the one you foun d in part a) ?
d) How many runner s would you need to weigh to find the 95% interval with a
margin of error equal to 1?
6. Basics of significance testing(Ch. 14)
A psychological test measures the motivation, attitu d e, and study habits of
college studen t s. Scores follow approxi ma t ely a Normal distribu tio n with mean
115 and standa r d deviation 25. You suspec t that inco ming fresh m e n have a
mean which is different from 115, because they are often excited yet anxious
about entering college. You give the test to 25 fresh m a n stud en t s and find their
mean score is 116.2. Is this data significan t at α = 0.05 level?