John has to complete a research project on the ape
population in Spain. He is trying to estimate the size of
population of apes. He randomly catches 37 apes and
marks them with paint. He releases apes in jungle.
The following year he observes 250 apes and he
found that 10 were marked with the paint that he used.
Find out the best estimate for the size of the ape
population?
The ratio of marked apes to total apes should be about the
same in both the sample population and the overall population.
Set up a proportion.
Number of marked Ape counted
Total number of Ape counted
=
Total number of marked Ape
Estimate of Ape population
Plug in the numbers you know and solve for
the Ape population, p.
10_ = 37
250
p
10p
10p == 37
9,250
x 250divide
(find the
cross
products)
both
sides
by 10.
P = 925
1) A famous television channel put tags on 58 alligator and
released them. Later, they catch 260 alligator; among those
alligator, 50 were tagged. Calculate the best estimate for the
alligator population?
50_ = 58
260
p
50 p =
260 x 58divide
(find the
cross
products)
both
sides
by 50.
50p
=15,080
P = 301.6
2) Management wants to open a cafeteria in the office building.
So they collected data from two random samples of 100
employees regarding employees’ office lunch preference?
Make at least two inferences based on the results.
Sample
Group
#1
#2
Corn Dog
Philly
Cheese
Steak
Reuben
Sandwich
Total
56
78
35
12
9
10
100
100
Sample
Group
#1
#2
Corn Dog
Philly
Cheese
Steak
Reuben
Sandwich
Total
56
78
35
12
9
10
100
100
1. Most employees prefer Corn Dogs.
2. More people prefer Corn Dogs more than Philly
Cheese Steaks and Reuben Sandwich combined.
3. Reuben sandwiches are not very popular.
3) A computer tracking chip company wants to test their chips.
They marked 32 birds by attaching computer chips to their legs.
Later on, they catch 440 birds, 28 of which are marked with
computer chips attached to them. They provided this data to
animal welfare authorities to estimate the bird population. To the
nearest whole number, what is the best estimate of the bird
population?
28_ = 32
440
p
28 p = 440
28p
14,080
x 32divide
(find the
cross
products)
both
sides
by 28.
P = 502.9
Mike is aTeam
statistician.
Heofwanted
Football
– Height
Playerstoincompare
inches the average height
of some of the players on his favorite baseball and football
teams.
football
characteristically played by larger
60, 62, Because
65, 74, 71,
69, 64,is67
athletes, he thinks that there will be a greater variability in the
heights ofTeam
football
players
compared
to baseball players. He
Baseball
– Height
ofas
Players
in inches
used the heights that were listed in the game time team
programs
determine
the75
heights of the players.
74,
73, 62,to68,
65, 70, 64,
2.
the height
difference
1. What
Whichisteam’s
average
playerbetween
is taller? the average players
on both teams?
2.
difference
players
is:
1.The
Theheight
mean
height of
ofaverage
the football
players
is 66.5 inches as
Baseball
average
height
– football
= height
difference
compared
to the
mean
heightaverage
of the height
baseball
players
at 68.875
68.875
inches
66.5 inches
= 2.375 player
inches is taller in this case.
inches.
The –average
baseball
3. The football team’s best three players are 62, 71,
and 74 inches tall. The baseball team’s best three
players are 68, 70, and 74 inches tall. Which team has
a greater variability of heights for their top 3 players?
Explain your answer.
The mean absolute deviation (MAD) tells us the degree
of variability of any data set. The greater the MAD
value, the more variability. We can calculate the MAD
for each set by:
1. Find the mean of each set:
Football: 62, 71, 74
Mean = (62 + 71+ 74) / 3 = 69
Baseball: 68, 70, 74
Mean = (68 + 70 + 74) / 3 = 70.67
2. Determine the deviation of each variable from the
mean:
Football: 62 – 69= -7
71 – 69= 2
Baseball: 68 – 70.67 = -2.67
74 – 69= 5
70 – 70.67= -.67
74 – 70.67= 3.33