A sociologist randomly selects 376 females 15 to 19 years old and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. Use the results in the accompanying table to complete the questions below. LOADING... Click the icon to view the data table of family structure and sexual activity. ​(a) Compute the

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A sociologist randomly selects
376
females 15 to 19 years old and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. Use the results in the accompanying table to complete the questions below.
LOADING...
Click the icon to view the data table of family structure and sexual activity.
​(a) Compute the expected values of each cell under the assumption of independence.
 
Had sexual intercourse
Both Biological or Adoptive Parents
Single Parent
Parent and
Stepparent
​Non-parental Guardian
 
Yes
34
nothing
44
nothing
60
nothing
64
nothing
 
No
16
nothing
34
nothing
41
nothing
83
nothing
​(Round to two decimal places as​ needed.)
 
​(b) Verify that the requirements for performing a​ chi-square test of independence are satisfied. Select all requirements for a​ chi-square test of independence.
 
 
A.
All expected frequencies are greater than or equal to 5.
 
B.
All expected frequencies are greater than or equal to 1.
 
C.
All expected frequencies are greater than or equal to 10.
 
D.
No more than​ 20% of the expected frequencies are less than 5.
 
E.
The expected frequencies are approximately Normal.
 
​(c) Test whether
family structure
and
sexual activity
of​ 15- to​ 19-year-old females are independent at the
α=0.1
level of significance. State the hypotheses. Choose the correct answer below.
 
A.
H0​:
Sexual activity and
family structure
are independent.
H1​:
Sexual activity and
family structure
are dependent.
 
B.
H0​:
μ1=E2
and
μ3=E3
and
μ3=E3
and
μ4=E4
H1​:
At least one mean is different from what is expected.
 
C.
H0​:
Sexual activity and
family structure
are dependent.
H1​:
Sexual activity and
family structure
are independent.
 
D.
H0​:
p1=p2=p3=p4
H1​:
At least one proportion is different from the others.
 
​(d) Compute the​ chi-square test statistic.
 
χ20=nothing
​(Round to three decimal places as​ needed.)
 
Determine the​ P-value.
 
​P-value=nothing
​(Round to three decimal places as​ needed.)
 
Make the proper conclusion. Choose the correct answer below.
 
 
A.
The​ P-value is
greater than
α​,
so
reject
H0.
There
is
sufficient evidence at the
α=0.05
level of significance to conclude that sexual activity and family structure are related.
 
B.
The​ P-value is
greater than
α​,
so
do not reject
H0.
There
is not
sufficient evidence at the
α=0.05
level of significance to conclude that sexual activity and family structure are related.
 
C.
The​ P-value is
less than
α​,
so
reject
H0.
There
is
sufficient evidence at the
α=0.05
level of significance to conclude that sexual activity and family structure are related.
 
D.
The​ P-value is
less than
α​,
so
do not reject
H0.
There
is not
sufficient evidence at the
α=0.05
level of significance to conclude that sexual activity and family structure are related.
 
 
 
 
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