Question

An amusement park would like to determine if they want to add in a new roller coaster. In order to decide whether or not they should add the new roller coaster, they poll people at the park to see how many rode the current roller coaster.

As people are leaving the park they randomly sample 600 people.
Out of the 600 people, 400 rode the roller coaster at the park.
Construct a 90% confidence interval to represent the proportion of riders who rode the roller coaster at the park. All conditions for inference have been met.

Answer 1

Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

• $\pi$ is the sample proportion.

• z is the critical value.

• n is the sample size.

In this problem, we have a 90% confidence level, hence$\alpha = 0.9$, z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$, so the critical value is z = 1.645.

The sample size and the estimate are given by:

$n = 600, \pi = \frac{400}{600} = 0.6667$

Hence, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 - 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6350$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 + 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6984$

The 90% confidence interval is given by: (0.6350, 0.6984).

More can be learned about the z-distribution at https://brainly.com/question/25890103

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