Respuesta :
Answer:
The calculated value Z = 0.063< 1.96 at 5% level of significance
Null hypothesis is accepted
There is no significant difference between age and watching television in teenagers
Step-by-step explanation:
Step(i):-
Given random sample size 'n' = 905
Given data 198 say they watch 3 or more hours of television per day.
Given random first sample size
n₁ = 905
First sample proportion
[tex]p_{1} = \frac{x_{1} }{n_{1} } = \frac{198}{905} = 0.2187[/tex]
Given random second sample size
n₂ = 503
second sample proportion
[tex]p_{2} = \frac{x_{2} }{n_{1} } = \frac{97}{503} = 0.1928[/tex]
Step(ii):-
Null Hypothesis : H₀
There is no significant difference between age and watching television in teenagers
Alternative Hypothesis :H₁
There is significant difference between age and watching television in teenagers
Step(iii):-
Test 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_{2} p_{2} }{n_{1}+n_{2} }[/tex]
[tex]P = \frac{905 X0.2187 + 503 X0.1928 }{905+503 }[/tex]
P = 0.2094
Q = 1 - 0.2094 = 0.7906
[tex]Z = \frac{0.2187-0.1928}{\sqrt{0.2094 X0.7906(\frac{1}{905} +\frac{1}{503} } )}[/tex]
on calculation , we get
Z = 0.063
The critical value Z₀.₀₅ = 1.96
The calculated value Z = 0.063< 1.96 at 5% level of significance
Conclusion:-
Null hypothesis is accepted
There is no significant difference between age and watching television in teenagers
