Respuesta :
Answer:
95% confidence interval for the proportion of all registered voters who will vote for candidate
(0.255 ,0.344)
The lower limit of the confidence interval is 0.255
Step-by-step explanation:
Explanation:-
Step1:-
Given data In a random sample of 400 registered voters, 120 indicate they plan to vote for Candidate.
n =400
The proportion of success [tex]p = \frac{120}{400}[/tex]
on calculation 'p' = 0.3
q =1-p
q = 1- 0.3 =0.7
Step2:-
95% confidence interval for the proportion of all registered voters who will vote for candidate
[tex](p - z_{\alpha } \sqrt{\frac{pq}{n} } , p+z_{\alpha } \sqrt{\frac{pq}{n} } )[/tex]
we use z- value =1.96 at 95% level of significance.
[tex](0.3 - 1.96\sqrt{\frac{(0.3)(0.7)}{400} } , 0.3+1.96\sqrt{\frac{0.3(0.7)}{400} } )[/tex]
on calculation , we get
(0.3 - 0.044 ,0.3+0.044)
(0.255 ,0.344)
conclusion:-95% confidence interval for the proportion of all registered voters who will vote for candidate
(0.255 ,0.344)
The lower limit of the confidence interval is 0.255
