A sociologist randomly selects 379 females 15 to 19 years old and asks each to d

Question

A sociologist randomly selects 379 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 parts (a) through (f) below (a) Compute the expected values of each cell under the assumption of independence Parent and Had sexual intercourse Both Biological or Adoptive P Single Parent Non-parental Guardian 62 59 46 18 85 37 No (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. B. The expected frequencies are approximately Normal. No more than 20% of the expected frequencies are less than 5 Data table of family structure and sexual activity C. All expected frequencies are greater than or equal to 1 D. All expected frequencies are greater than or equal to 10. E. All expected frequencies are greater than or equal to 5. Had sexual Both Biological orSingle Parent intercourse Adoptive Parents Parent and Stepparent 59 | Non-parental Guardian 46 37 (c) Compute the chi-square test statistic. Yes No 31 18 62 85 -D (Round to three decimal places as needed.) Click to select your answer(s). PrintDone

Explanation / Answer

Given table data is as below

------------------------------------------------------------------

calculation formula for E table matrix

------------------------------------------------------------------

expected frequecies calculated by applying E - table matrix formulae

------------------------------------------------------------------

calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

------------------------------------------------------------------

set up null vs alternative as

null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

level of significance, = 0.1

from standard normal table, chi square value at right tailed, ^2 /2 =6.251

since our test is right tailed,reject Ho when ^2 o > 6.251

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 10.524

critical value

the value of |^2 | at los 0.1 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 4 - 1 ) = 1 * 3 = 3 is 6.251

we got | ^2| =10.524 & | ^2 | =6.251

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0.015

ANSWERS

---------------

b.

expected frequncies are approximately normal

all expecetd frequqnceis are greater than eaual to 5

c.

test statistic: 10.52

d.

null, Ho: sexual activity and family structure are independent

alternative, H1: sexual activity and family structure are dependent

e.

p-value:0.015

decision: the p valu eis greater than alpha, so reject Ho. there is suffcient evidence that at alpha = 0.05 LOS to conclude that sexual and family are releated

MATRIX col1 col2 col3 col4 TOTALS row 1 31 62 59 46 198 row 2 18 85 41 37 181 TOTALS 49 147 100 83 N = 379

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.