Question

To design a new advertising campaign, Ford Motor Company would like to estimate the proportion of drivers of the new Ford Fusion that are women. In a random sample of 81 Fusion owners, 48 of them were women. What is the 90% confidence interval estimating the proportion of all drivers who are women?

Answer 1

Solution :

Given that,

n = 81

x = 48

Point estimate = sample proportion = = x / n = 48/81=0.593

1 -   = 1-0.593 =0.407

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.593*0.407) /81 )

E = 0.0898

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.593- 0.0898< p <0.593+ 0.0898

0.5032< p < 0.6828

The 90% confidence interval for the population proportion p is : 0.5032, 0.6828