Question

A zoo in a major city is contemplating whether to install a digital system, which will allow the visitors to get information about a particular attraction at the touch of a digital code through a device they will rent. It is anticipated that this device will rent for $3 each. Based on this rental price, a financial analyst for the zoo indicates that if more than 10% of the zoo visitors rent the system, the rental revenue will more than offset the installation cost of the system and the zoo will make a profit. To help make the decision, a random sample of 400 zoo visitors were given the details of the system capabilities and rental cost and were asked whether they will rent such a device or not.

1. If 45 people say that they will rent such a device, construct a 98% confidence interval for the proportion (p) of the zoo visitors who will rent this device. What does this interval means?

Answer 1

Sample proportion=45/400=0.1125

98% confidence interval for the

=0.1125+/-2.326*sqrt(0.1125*(1-0.1125)/400)

=0.1125+/-0.0367

=(0.0758, 0.1492)

We are 98% confident that true proportion (p) of the zoo visitors who will rent this device falls between 0.0758 and 0.1492

As,lower limit is lower than 10% we can not say that more than 10% of the zoo visitors rent the system.