Question

A car company took a random sample of 85 people and asked them whether they have a plan to purchanse an electrinic car in the near future. 18 of them responded that they have a plan to buy one, what is the error term of a 96% confidence interval from the population proportion of people having a plan to buy an electrinuc car?

Answer 1

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:

$\hat p = \frac{X}{n}= \frac{18}{85}=0.212$

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 $\alpha=1-0.96=0.04$ and $\alpha/2 =0.02$. And the critical value would be:

$z_{\alpha/2}=-2.05, z_{1-\alpha/2}=2.05$

The confidence interval for the true proportion is given by this expression:  

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Replacing the data given we got:

$0.212 - 2.05\sqrt{\frac{0.212(1-0.212)}{85}}=0.121$

$0.212 + 2.05\sqrt{\frac{0.212(1-0.212)}{85}}=0.303$

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).