Answer :
Answer:
H0 is accepted
there is no difference between the proportions of Indian and Asian young people who listen to rap music every day.
Step-by-step explanation:
Given a sample survey compared 634 randomly chosen Indians aged 15 to 25 with 567 randomly selected Asians in the same age group.
[tex]p_{1} = \frac{368}{634} =0.580[/tex]
It found that 368 of the Indians and 130 Asians listened to rap music every day.
[tex]p_{2} = \frac{130}{567} =0.229[/tex]
Null hypothesis H0: there is no difference between the proportions of Indian and Asian young people who listen to rap every day.
[tex]p_{1} = p_{2}[/tex]
Alternative hypothesis:- [tex]p_{1} \neq p_{2}[/tex]
Level of significance α = 0.05
The test of statistic
[tex]z = \frac{p_{1} - p_{2}}{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} }) } } }[/tex]
where [tex]p = \frac{n_{1}p_{1} + n_{1}p_{2}}{n_{1}+n_{2}} = \frac{634(0.580)+567(0.229)}{634+567}[/tex]
p = 0.414
and q = 1-p = 1- 0.414 =0.586
[tex]Z = \frac{0.580-0.229}{\sqrt{0.414(0.586)(\frac{1}{634} +\frac{1}{567} } } }[/tex]
on calculation , we get
z = 0.300 ><1.96 at 95 % level of significance
H0 is accepted
there is no difference between the proportions of Indian and Asian young people who listen to rap every day.