IIT Relationship Between the Duration of IUD Use to Infertility Worksheet The statistic question has been solved… only write SAS program……………..

IIT Relationship Between the Duration of IUD Use to Infertility Worksheet The statistic question has been solved… only write SAS program……………………………………………………. 4. A study performed in 1985 investigated the relationship between the duration of IUD
use to infertility. A group of 89 infertile IUD users and a group of 640 control IUD users
were identified and then further categorized (or subdivide) by the duration of IUD use.
The data are presented in the table below
< 3 months infertile IUD users 3-18 months 18-36 months > 36
months
10
23
20
36
89
53
200
168
219
640
223
188
255
729
(cases)
fertile IUD
users
(controls)
63
a. What is the appropriate name of the statistical test you will use to carry out
this research question?
Chi-square test of variable independence
b. What is the Null and alternative hypothesis?
Null Hypothesis
Duration of IUD use and infertility are independent.
Alternate Hypothesis
Duration of IUD use and infertility are not independent.
c. Calculate the expected counts under the null hypothesis.
Expected counts:
< 3 months infertile IUD users 3-18 months 18-36 months > 36 months
7.69
27.22
22.95
31.13
55.31
195.78
165.05
223.87
(cases)
fertile IUD
users
(controls)
d. Calculate the test statistic
? 2 Test statistic
r
k
= ??
i =1 j =1
(O
ij
? Eij )
2
Eij
(10 ? 7.69) 2 (23 ? 27.22) 2
(219 ? 223.87) 2
+
+ …. +
7.69
27.22
223.87
= 2.8358
=
e. What is your conclusion at the 0.01 significance level- state it in words in the
context of the problem?
The table includes r=2 rows and k=4 columns, so the number of degrees of freedom
for the test is df = (2 ? 1)( 4 ? 1) = 3 . For the 0.01 level of significance and df = 3 , the
critical value of chi-square is 11.345.The calculated chi-square (2.8358) is less than
the critical value (11.345), so the null hypothesis cannot be rejected at the 0.01 level.
From this analysis it appears that duration of IUD and infertility are independent.
Write a SAS program to carry out this hypothesis test and check your answers.

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