Data Scholars Midterm Review Worksheet
October 9, 2023
4.
Stars (Fall 2022, Midterm - Hypothesis Testing)
You
read
online
that
the
Milky
Way
galaxy
contains
100
billion
active
stars
, 10
billion
white
dwarf
stars
,
and
1
billion
neutron
stars
.
You
also
find
the
following
near
-
Earth
dataset
online
:
within
300
trillion
kilometers
(10
parsecs
)
of
Earth
,
there
are
392
active
stars
and
21
white
dwarf
stars
,
but
0
neutron
stars
.
(b) (8.0 points)
You decide to use these data to investigate whether the distribution of stars (active stars, white dwarf stars,
and neutron stars) near Earth is the same as the distribution across the galaxy or whether it’s unusual.
i. (2.0 pt)
Complete this
null
hypothesis:
The distribution of stars. . .
#
#
#
near Earth has exactly the same proportions as the galaxy’s distribution.
near Earth is like a random sample from the galaxy’s distribution.
in a randomly selected region of the Milky Way is the same as the galaxy’s distribution.
in every sample of stars is the same as the galaxy’s distribution.
ii. (2.0 pt)
Complete this
alternative
hypothesis:
The distribution of stars near Earth. . .
#
#
#
is the same as the galaxy’s distribution.
is consistent with the galaxy’s distribution.
is not like a random sample from the galaxy’s distribution.
is not the same as the distribution from a randomly selected region of the galaxy.
iii. (2.0 pt)
Which test statistic is best for choosing between these null and alternative hypotheses?
#
#
#
Total variation distance from the galaxy’s distribution
Di
ff
erence between the number of neutron stars in the sample and the galaxy
Di
ff
erence between the proportion of neutron stars in the sample and the galaxy
Di
ff
erence between the sizes of the samples
iv.
(2.0 pt)
Under the null hypothesis, what would best explain the fact that near Earth there are 0
neutron stars?
#
#
The number of stars near Earth is small.
Neutron stars are dim and hard to observe.
#
Neutron stars are mostly near the center of the galaxy and Earth is not.
Due to random chance, there happen to be 0 neutron stars near Earth.
