A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year.
A) [0.3152, 0.3648]
B) [0.3192, 0.3608]
C) [0.3394, 0.3406]
D) [0.3354, 0.3446]

Question

Quizplus · Accepted Answer

To construct a confidence interval for a proportion, we use the formula:

sample proportion ± z*standard error

where the standard error is:

√[(sample proportion)*(1-sample proportion)/n]

In this case, the sample proportion is 0.34 and the sample size is 1,400.

To find the z-value for a 90% confidence interval, we look up the corresponding value in a standard normal table or use a calculator, and we find that z = 1.645.

Plugging in the numbers, we get:

0.34 ± 1.645*√[(0.34)*(1-0.34)/1,400]

Simplifying this expression, we get:

0.34 ± 0.021

So the confidence interval is:

[0.319, 0.361]

Therefore, the best choice is B.

A Sample of 1,400 American Households Was Asked If They