Solve the problem.
-When 306 college students are randomly selected and surveyed, it is found that 115 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
A)0.305

Question

Solve the problem.
-When 306 college students are randomly selected and surveyed, it is found that 115 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
A)0.305 < p < 0.447
B)0.311 < p < 0.440
C)0.330 < p < 0.421
D)0.322 < p < 0.430

Quizplus · Accepted Answer

To find a 99% confidence interval for the proportion of all college students who own a car, we use the formula for the confidence interval for a proportion: $$p \pm z\sqrt{\frac{p(1-p)}{n}}$$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level, and $n$ is the sample size.Given:- $n = 306$ (sample size)- $115$ out of $306$ students own a car, so $p = \frac{115}{306} \approx 0.376$.For a 99% confidence level, the z-score is approximately $2.576$.Plugging these values into the formula:$$0.376 \pm 2.576\sqrt{\frac{0.376(1-0.376)}{306}}$$Calculating the margin of error:$$2.576\sqrt{\frac{0.376(0.624)}{306}} \approx 0.071$$Therefore, the 99% confidence interval is approximately:$$0.376 - 0.071 < p < 0.376 + 0.071$$$$0.305 < p < 0.447$$Hence, the correct choice is A) 0.305 < p < 0.447.

Solve the Problem. -When 306 College Students Are Randomly Selected and Surveyed, It