A sociologist randomly selects376females 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 intercourseBoth Biological or Adoptive ParentsSingle ParentParent andStepparentNon-parental Guardian Yes34nothing44nothing60nothing64nothing No16nothing34nothing41nothing83nothing(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 whetherfamily structureandsexual activityof 15- to 19-year-old females are independent at theα=0.1level of significance. State the hypotheses. Choose the correct answer below. A.H0:Sexual activity andfamily structureare independent.H1:Sexual activity andfamily structureare dependent. B.H0:μ1=E2andμ3=E3andμ3=E3andμ4=E4H1:At least one mean is different from what is expected. C.H0:Sexual activity andfamily structureare dependent.H1:Sexual activity andfamily structureare independent. D.H0:p1=p2=p3=p4H1: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 isgreater thanα,sorejectH0.Thereissufficient evidence at theα=0.05level of significance to conclude that sexual activity and family structure are related. B.The P-value isgreater thanα,sodo not rejectH0.Thereis notsufficient evidence at theα=0.05level of significance to conclude that sexual activity and family structure are related. C.The P-value isless thanα,sorejectH0.Thereissufficient evidence at theα=0.05level of significance to conclude that sexual activity and family structure are related. D.The P-value isless thanα,sodo not rejectH0.Thereis notsufficient evidence at theα=0.05level of significance to conclude that sexual activity and family structure are related.

Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have solved only the first three subparts for you. If you need any specific subpart to be answered, please re-submit the question by specifying the subpart number or name. (a). Compute the expected values of each cell: The row totals and column totals need to be calculated to perform chi-square test for independence. Denote oij as the observed frequency for ith row and jth column (i =1, 2 ; j =1, 2, 3). Denote eij as the expected frequency for ith row and jth column (i =1, 2 ; j =1, 2, 3). Table 1: This table provides the data values, oij. The general formula to obtain the expected frequency is given below: Now the expected frequencies have to be calculated under the independence assumption. If independent, eij = (oi∙) ∙ (o∙j) / N. [o∙j = column total of jth column, N = grand total of all observations = 376]. The expected frequency for the first cell is obtained as given below: Similarly, the remaining expected frequencies are obtained in the table given below:(b). Verify the requirements for performing a chi-square test of independence: The necessary assumptions for Chi-square test of independence are given below: The data in the cells should represent frequencies or counts. The sample should be collected using simple random sampling. Each subject should contribute only into any of the cells. The study groups should be independent of each other. The expected value of each cell should not be less than 5. Here, the cells are representing the frequencies. In the given scenario: The simple random sampling method is used in the given scenario. The variables involved in the study are categorical. The subjects in each group are not related. The expected frequency count for each cell of the given contingency table is at least 5. All expected frequencies are greater than or equal to 5. (c). State the test hypotheses: The two categories of interest are the “Sexual activity” and “Family structure”. The researcher is specially interested to test whether there is an association between the categories “Sexual activity” and “Family structure”. Thus, the study seeks to find whether there is any association between the two categories “Sexual activity” and “Family structure”. In other words, the study aims to test whether the two categories ““Sexual activity” and “Family structure” are independent or not, using a Chi-square test of Independence. The hypotheses to be tested are: Null hypothesis: H0: The two categories “Sexual activity” and “Family structure” are independent. Alternative hypothesis: Ha: The two categories “Sexual activity” and “Family structure” are dependent.

Answered: A sociologist randomly selects 376…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.

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.

All expected frequencies are greater than or equal to 5.

All expected frequencies are greater than or equal to 1.

All expected frequencies are greater than or equal to 10.

No more than 20% of the expected frequencies are less than 5.

The expected frequencies are approximately Normal.

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.

H0:

Sexual activity and

family structure

are independent.

H1:

Sexual activity and

family structure

are dependent.

H0:

μ1=E2

and

μ3=E3

and

μ3=E3

and

μ4=E4

H1:

At least one mean is different from what is expected.

H0:

Sexual activity and

family structure

are dependent.

H1:

Sexual activity and

family structure

are independent.

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.

The P-value is

greater than

α,

reject

H0.

There

sufficient evidence at the

α=0.05

level of significance to conclude that sexual activity and family structure are related.

The P-value is

greater than

α,

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.

The P-value is

less than

α,

reject

H0.

There

sufficient evidence at the

α=0.05

level of significance to conclude that sexual activity and family structure are related.

The P-value is

less than

α,

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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