In: Statistics and Probability
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 .
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