Question

Furniture Land surveyed 640 consumers and found that 478 were enthusiastic about a new home dècor it plans to show in its store in High Point.

Construct the 98% 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 = 640

x = 478

Point estimate = sample proportion = = x / n = 478/640=0.747

1 -   = 1- 0.747 =0.253

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

= 2.326 (((0.747*0.253) / 640)

E = 0.040

A 98% confidence interval proportion p is ,

- E < p < + E

0.747-0.040 < p < 0.747+0.040

0.707 , 0.787

Confidence interval for the population proportion is 0.707and 0.787