# Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new dru - Mathematics and Statistics

Sum

Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new drug, 10 persons were not attacked by influenza: Prepare to compute the χ2 square statistic.

#### Solution

The observed frequency table can be prepared as follows:

 Drug administered Drug not administered Row total (Ri) Attacked 18 30 48 Not Attacked 62 10 72 Column total (Cj) 80 40 120

Expected frequencies are given by

Eij = ("R"_"ij"xx"C"_"ij")/"N"

E11 (48xx80)/120 = 32

E12 = (48xx40)/120 = 16

E21 = (72xx80)/120 = 48

E22 = (72xx40)/120 = 24

Table of expected frequencies.

 Drug administered Drug not administered Total Attacked 32 16 48 Not Attacked 48 24 72 Total 80 40 120

Now.

χ2 = sum[(("O"_"ij"- "E"_"ij")^2)/"E"_"ij"]

= (18-32)^2/32+(30-16)^2/16+(62-48)^2/48+(10-24)^2/24

= 196/32+196/16+196/48+196/24

= 6.125 + 12.25 + 4.083 + 8.167

= 30.625

Concept: Chi-Square Statistic ( χ2 )
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic
Exercise 4.2 | Q 5. (b) | Page 53