Name:
Hour:
Date:
Are Taco Tongue and Evil Eyebrow independent?
Is there an association between the Taco Tongue and the Evil Eyebrow? Below is the data
for a random sample of 600 Senior students. Do we have convincing evidence that the
ability to do the Taco Tongue and Evil Eyebrow are associated for all Seniors?
AlB)
1. Describe what it means for two events to be independent.
whether or not one event occurs
BY
Al
=p(
=p(
A)
Knowing
the probability
of the other event
.
Excpoegnted rowtotaxdumntotal
grand total
,
2. Calculate the expected counts.
p(
does not change
Observed:
Expected:
320
80
160
40
3. Do the data provide significant evidence that there is an association between the ability to Taco
Tongue and Evil Eyebrow for all Seniors? Use α = 0.05
STATE: Hypotheses:
Significance level: 0=0.05
Ho: Taco Tongue and Evil Eyebrow are not associated for all seniors (independent)
Hai Taco Tongue and Evil Eyebrow are associated for all Seniors (not independent)
PLAN: Name of procedure: chi-square test for independence
Random:
lot
:
"
Check conditions:
random sample of 600 Seniors
"
600 E tho (all seniors ) → so
All
Large counts
:
DO:
s
so we can
Specific Formula:
x:
Work:
shoes
-
-
-
so
distribution .in
.
XZ
the sampling
E
2/2=480,66-605+103%-207:(2%405+400-805
Picture:
tm
5
.
T
00
X'
2/3-18.75×2=18.75
p value
=
2.5+1.25-110+5
Test statistic:
P-value:
Ho
Interpret
Assuming
pwawe
CONCLUDE:
person
getting
we
a
is true
reject
Ho and
follow
a
follow up : The
,
there is
a
0.000015
or
0.000015
probability
of
.
.
an
Eyebrow for all seniors
number of No TTAes EE was
Evil
=
-
greater purely by chance Because 0 00001560.05
's between
association
do have
convincing evidence of
XZ of 18.75
conclusionTaco Tongue
'D
(no association)
-
wtoithpofffefgtaieomer.to/df=G-D(2-D=I
sampling
S (see table)
counts
expected
Z
df Crows Dx (columns
generalize
.
much lower than
expected
.
D
Name:
Hour:
Date:
Chi-Square Test for Independence
( .gr#os.mogeunaeritaGieommibears Xteslk Which X ?
X2GOf(Moms)
I sample ,1variable
'
Important ideas:
HIT X' test for independence
Ho : There
is not
an
association
between
"
between
Ha:
tests
independence ( Taeko.EE?yebrow)
sample , 2 variables
for
1-
Check Your Understanding
For each of the following situations decide what type of chi square test is appropriate. Explain.
1. A random sample of 200 students was asked to sample a new type of pizza that the school was
considering using as a replacement for the current pizza. Each student stated if they were a
freshman, sophomore, junior, or senior and also if they liked the new pizza more than the current
pizza (or not). The school would like to know if there is a relationship between grade level and
pizza opinion.
-
1-
sample
X' test for independence
2 variables ( grade level , pizza
opinion)
2. Another school is also considering changing their pizza vendor. This school selects a random
sample of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. Each student tries the new
pizza and states whether they like it more than the current pizza (or not). The school would like
to know if the distribution of opinion differs across the grade levels.
4
samples
X' test
for
homogeneity
1- variable (pizza opinion)
3. A pizza shop claims that 30% of orders are placed on Fridays, 20% are placed on Saturdays,
and 10% of orders are placed on the other days of the week. A global pandemic may have
changed this distribution. The manager investigates so he knows how to staff the pizza shop
appropriately. He selects a random sample of 300 orders and classifies each one according to
the day of the week the order was placed. He wants to know if the distribution of orders is the
same as it was before the global pandemic.
1-
sample
X' test for
7- variable ( day of order)
goodness
Offit