Respuesta :
Answer: We conclude that we have evidence to support the claim of 29% .
95 % confidence interval estimate of the population percentage of candies that are red: (0.141,0.447)
Step-by-step explanation:
The confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Given :- Sample size :[tex]n=34[/tex]
Number of red candies = 10
Proportion of red candies in sample : [tex]\hat{p}=\dfrac{10}{34}\approx0.294[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Now, the 95 % confidence interval estimate of the population percentage of candies that are red will be :-
[tex]0.294\pm (1.96)\sqrt{\dfrac{0.294(1-0.294)}{34}}\\\\\\\approx0.294\pm0.153\\\\=(0.294-0.153,0.294+0.153)\\\\=(0.141,0.447)[/tex]
Since , [tex]0.29\ \epsilon\ (0.141,0.447)[/tex]
Therefore, we conclude that we have evidence to support the claim.
We conclude that we have evidence to support the claim of [tex]29[/tex] % .
[tex]95%[/tex] % confidence interval estimate of the population percentage of candies that are red: [tex](0.141,0.447)[/tex]
The confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z_{\alpha /2}{\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}}[/tex]
Given :- Sample size : [tex]n=34[/tex]
Number of red candies =[tex]10[/tex]
Proportion of red candies in sample : [tex]\hat{p}=\frac{10}{34}\approx 0.294[/tex]
Significance level : [tex]\alpha =1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha /2}=1.96[/tex]
Now, the [tex]95[/tex] % confidence interval estimate of the population percentage of candies that are red will be :-
[tex]0.294\pm (1.96)\sqrt{\frac{0.294(1-0.294)}{34}}[/tex]
[tex]\approx 0.294\pm 0.153\\ \\ =(0.294-0.153,0.294+0.153)\\ \\ =(0.141,0.447)[/tex]
Learn more about probability.
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