In: Statistics and Probability
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.
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)