The University of Delaware would like to estimate the propor

The University of Delaware would like to estimate the proportion of fans who purchaseconcessions at the first basketball game of of the new season. The basketball facility has a capacity of 3500people and is routinely sold out. It was discovered that atotal of 260 fans out of a random sample of 400 purchased concessions during the game.

1. Construct a 95% confidence interval to estimate the proportion of fans who purchasesd concessions during the game.

Solution

Confidence Interval Estimate for the Proportion

Data

Sample Size

400

Number of Successes

260

Confidence Level

95%

Intermediate Calculations

Sample Proportion

0.65

Z Value

1.96

Standard Error of the Proportion

0.0238

Interval Half Width

0.0467

Confidence Interval without Finite Population correction

Interval Lower Limit

0.6033

Interval Upper Limit

0.6967

Confidence Interval with Finite Population correction

Population Size

3500

FPC Factor

0.9413

Interval Half Width

0.0440

Interval Lower Limit

0.6060

Interval Upper Limit

0.6940