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Family Structure and Sexual ActivityA sociologist wants to
Chapter , Problem 7AYU(choose chapter or problem)
Problem 7AYU
Family Structure and Sexual ActivityA sociologist wants to discover whether the sexual activity of females between the ages of 15 and 19 years of age and family structure are associated. She randomly selects 380 females between the ages of 15 and 19 years of age and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. The results are shown in the table. Data are based on information obtained from the U.S. National Center for Health Statistics
Family Structure | ||||
|
Had Sexual Intercourse |
Both Biological or Adoptive Parents |
Single Parent |
Parent and Stepparent |
Nonparental Guardian |
Yes |
64 |
59 |
44 |
32 |
No |
86 |
41 |
36 |
18 |
(a) Compute the expected values of each cell under the assumption of independence.
(b) Verify that the requirements for performing a chi-square test of independence are satisfied.
(c) Compute the chi-square test statistic.
(d) Test whether family structure and sexual activity of 15- to 19-year-old females are independent at the α = 0.05 level of significance.
(e) Compare the observed frequencies with the expected frequencies. Which cell contributed most to the test statistic? Was the expected frequency greater than or less than the observed frequency? What does this information tell you?
(f) Construct a conditional distribution by family structure and draw a bar graph. Does this evidence support your conclusion in part (d)?
Questions & Answers
QUESTION:
Problem 7AYU
Family Structure and Sexual ActivityA sociologist wants to discover whether the sexual activity of females between the ages of 15 and 19 years of age and family structure are associated. She randomly selects 380 females between the ages of 15 and 19 years of age and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. The results are shown in the table. Data are based on information obtained from the U.S. National Center for Health Statistics
Family Structure | ||||
|
Had Sexual Intercourse |
Both Biological or Adoptive Parents |
Single Parent |
Parent and Stepparent |
Nonparental Guardian |
Yes |
64 |
59 |
44 |
32 |
No |
86 |
41 |
36 |
18 |
(a) Compute the expected values of each cell under the assumption of independence.
(b) Verify that the requirements for performing a chi-square test of independence are satisfied.
(c) Compute the chi-square test statistic.
(d) Test whether family structure and sexual activity of 15- to 19-year-old females are independent at the α = 0.05 level of significance.
(e) Compare the observed frequencies with the expected frequencies. Which cell contributed most to the test statistic? Was the expected frequency greater than or less than the observed frequency? What does this information tell you?
(f) Construct a conditional distribution by family structure and draw a bar graph. Does this evidence support your conclusion in part (d)?
ANSWER:Answer :
Step 1
Given a sociologist wants to discover whether the sexual activity of females between the ages of 15 and 19 years of age and family structure are associated. She randomly selects 380 females between the ages of 15 and 19 years of age and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse.
The equated frequency are
|
Both Biological or Adoptive Parents |
Single Parent |
Parent and Stepparent |
Nonparental Guardian |
Total |
|
Yes |
64 |
59 |
44 |
32 |
199 |
No |
86 |
41 |
36 |
18 |
181 |
Total |
150 |
100 |
80 |
50 |
380 |