In a survey 260 students in a high school were asked where t

In a survey, 260 students in a high school were asked where they prefer to do their holiday shopping. Possible responses were \'online\' and \'in a store\'. The students were also categorized as male or female. The following table records the data collected. What proportion of students answered that they prefer to shop for gifts online? What proportion of students are females and prefer to shop in store? What proportion of female students answered that they prefer to shop for gifts online? What proportion of male students answered that they prefer to shop for gifts online? Based on the findings above, can we conclude that gender has an effect on gift shopping preferences? Explain.

Solution

there are 260 students in all out of which 161 are female and 99 are male

231 prefers online shopping and 29 prefers in store shopping

number of students who are female and prefer online shopping=143

number of students who are female and prefer at store shopping=18

number of students who are male and prefer online shopping=88

number of students who are male and prefer at store shopping=11

a) proportion of students answered that they prefer to shop gifts online

=number of students prefer to shop gifts online/total number of students=231/260=0.88846 [answer]

b) proportion of students who are female and prefer to shop in store

= number of students who are female and prefer to shop in store/total number of students=18/260=0.069

c) proportion of female students who answered that they prefer to shop for online gifts

=number of students who are female and prefer to shop online/total number of female students=143/161=0.888198

d) proportion of male students who answered that they prefer to shop for online gifts
=number of students who are male and prefer to shop online/total number of male students=88/99=0.8889

e) if gender has no effect on gift shopping preferences then these two attributes A=gender and B=gift shopping preferences would be independent.

and if A and B are independent then f_AB-f_A*f_B/n=0 for all values of A and B

where n= total number of students=260

f_AB=number of students having characteristic A and B

f_A=number of students having characteristic A

f_B=number of students having characteristic B

now A has two forms a1=female   a2=male

B has two forms b1=prefer online shopping   b2=prefer in shop shopping

so f_a1b1-f_a1*f_b1/n=143-161*231/260=-0.0423

f_a1b2-f_a1*f_b2/n=18-161*29/260=0.0423

f_a2b1-f_a2*f_b1/n=88-99*231/260=0.0423

f_a2b2-f_a2*f_b2/n=11-29*99/260=-0.0423

so the values are very low. but not equal to zero.

so Yule\'s coefficient of association is

Q_AB=(f_a1b1*f_a2b2-f_a1b2*f_a2b1)/(f_a1b1*f_a2b2+f_a1b2*f_a2b1)=(143*11-88*18)/(143*11+88*18)=-0.00348

which is negative and very low value.

hence the conclusion is that gender has a very vey small negative effect on gift shopping.

i.e, females are likely to prefer online gift shopping more than the males but this association is very very low . so it can be claimed that approximately gender has no effect on gift shopping preferences.