Question

The manager of JAX, a local food restaurant, is concerned about customers who ask for a water cup when placing an order but fill the cup with Dr. Pepper (this is Texas), instead of filling the cup with water. The manager selected a random sample of 80 customers who asked for a water cup when placing an order and found that 23 of those customers filled the cup with a soft drink from beverage fountain.  

Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with Dr. Pepper.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 23 / 80 = 0.288

1 - = 1 - 0.288 = 0.712

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.288 * 0.712) / 80)

= 0.099

A 95% confidence interval for population proportion p is ,

± E   

= 0.288  ± 0.099

= ( 0.189, 0.387 )

We are 95% confident that the true proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with Dr. Pepper is between 0.189 and 0.387.