Question

In a survey, 600 consumers were asked whether they would like to purchase a domestic or a foreign made automobile. 340 said that they preferred to purchase a domestic made automobile. Construct and explain a 95% confidence interval estimate for the proportion of all consumers who prefer domestic automobiles.

Answer 1

Solution :

Given that,

n = 600

x = 340

Point estimate = sample proportion = = x / n = 340/600=0.567

1 -   = 1- 0.567 =0.433

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.567*0.433) /600 )

E = 0.0396

A 95% confidence interval is ,

- E < p < + E

0.567-0.0396 < p < 0.567+0.0396

0.5274< p < 0.6066

(0.5274 , 0.6066)