Question

Furniture Land surveyed 520 consumers and found that 456 were enthusiastic about a new home dècor it plans to show in its store in High Point.

Construct the 99% confidence interval for the population proportion. (Round the final answers to 3 decimal places.)

Confidence interval for the population proportion is and .

Answer 1

Solution :

Given that,

n = 520

x = 456

= x / n = 456 / 520 = 0.877 (rounded)

1 - = 1 - 0.877 = 0.123

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* (((0.877 * 0.123) / 520) = 0.037

A 90 % confidence interval for proportion p is ,

- E < P < + E

0.877 - 0.037 < p < 0.877 + 0.037

0.840 < p < 0.914

The 90% confidence interval for the population proportion p is : ( 0.840 , 0.914)