MATH SOLVE

3 months ago

Q:
# The data given to the right includes data from 34 candies, and 10 of them are red. The company that makes the candy claims that 29% of its candies are red. Use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 29%? Construct a 95 % confidence interval estimate of the population percentage of candies that are red.

Accepted Solution

A:

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 = 10Proportion 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.