Respuesta :
Answer:
We have 96% of confidence that the true proportion of people who responded that they have a plan to buy one electric car is between (0.121 and 0.303).
Step-by-step explanation:
For this case the estimated proportion of people who responded that they have a plan to buy one electric car is given by:
[tex]\hat p = \frac{X}{n}= \frac{18}{85}=0.212[/tex]
Where X represent the number of people who responded that they have a plan to buy one and n represent the sample size selected
We know that the confidence level for this case is 96% of confidence, then our significance level would be [tex]\alpha=1-0.96=0.04[/tex] and [tex]\alpha/2 =0.02[/tex]. And the critical value would be:
[tex]z_{\alpha/2}=-2.05, z_{1-\alpha/2}=2.05[/tex]
The confidence interval for the true proportion is given by this expression:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing the data given we got:
[tex]0.212 - 2.05\sqrt{\frac{0.212(1-0.212)}{85}}=0.121[/tex]
[tex]0.212 + 2.05\sqrt{\frac{0.212(1-0.212)}{85}}=0.303[/tex]
We have 96% of confidence that the true proportion of people who responded that they have a plan to buy one electric car is between (0.121 and 0.303).
