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 98% confidence interval of the proportion of American households who expect to buy a new car next year.
A) [0.3074, 0.3726]
B) [0.3105, 0.3695]
C) [0.3140, 0.3660]
D) [0.3392, 0.3408]

Question

Quizplus · Accepted Answer

To find the confidence interval, we first find the standard error of the sample proportion:

SE = sqrt[(p-hat*(1-p-hat))/n] 
SE = sqrt[(0.34*0.66)/1400] 
SE = 0.016

Next, we find the margin of error:

ME = z*SE 
ME = 2.33*0.016 
ME = 0.037

Finally, we construct the interval:

p-hat +/- ME 
0.34 +/- 0.037 
[0.3105, 0.3695]

Therefore, the best choice is B.

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