A recent survey asked adults about their beliefs about premarital sex and whethe
ID: 3319816 • Letter: A
Question
A recent survey asked adults about their beliefs about premarital sex and whether they thought birth control should be made available to teenagers. The data are below. Test whether beliefs about premarital sex and beliefs about birth control are independent using a 5% significance level. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.
Teenage Birth Control
Premarital Sex
Disagree
No Opinion
Agree
Total
Always wrong
68
60
38
166
Sometimes Wrong
41
74
42
157
Not wrong
57
161
157
375
Total
166
295
237
698
Teenage Birth Control
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:beliefs about premarital sex and beliefs about birth control are independent
alternative, H1: beliefs about premarital sex and beliefs about birth control are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =9.488
since our test is right tailed,reject Ho when ^2 o > 9.488
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 50.267
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 9.488
we got | ^2| =50.267 & | ^2 | =9.488
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0
ANSWERS
---------------
null, Ho:beliefs about premarital sex and beliefs about birth control are independent
alternative, H1: beliefs about premarital sex and beliefs about birth control are dependent
test statistic: 50.267
critical value: 9.488
p-value:0
decision: reject Ho
have evidence that beliefs about premarital sex and beliefs about birth control are dependent
MATRIX col1 col2 col3 TOTALS row 1 68 60 38 166 row 2 41 74 42 157 row 3 57 161 157 375 TOTALS 166 295 237 N = 698