Question

Based on a sample of 290 people, 214 said they prefer "Trydint" gum to "Eklypse".

The point estimate is: ____ (to 3 decimals)

The 99 % confidence interval is: __ to ___ (to 3 decimals)

Answer 1

Solution :

Given that,

n = 290

x = 214

= x / n = 214 / 290 = 0.738

The point estimate is 0.738

1 - = 1 - 0.738 = 0.262

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.738 * 0.262) / 290)

= 0.067

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.738 - 0.067 < p < 0.738 + 0.067

0.671 < p < 0.805

The 99% confidence interval for the population proportion p is : ( 0.671 , 0.805)