Question

Furniture Land surveyed 550 consumers and found that 478 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 = 550

x = 478

Point estimate = sample proportion = = x / n = 478/550=0.869

1 -   = 1- 0.869 =0.131

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.869*0.131) / 550)

E = 0.037

A 99% confidence interval for proportion p is ,

- E < p < + E

0.869-0.037 < p < 0.869+0.037

0.832< p < 0.906

Confidence interval for the population proportion is 0.832 and 0.906