Exhibit 8-6.A sample of 1400 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. Refer to Exhibit 8-6.Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we can use the formula:

CI = p̂ ± zα/2 √((p̂*(1-p̂))/n)

where: 
p̂ = sample proportion = 0.34
n = sample size = 1400
zα/2 = critical value at 98% confidence level = 2.33

Plugging in the values, we get:

CI = 0.34 ± 2.33 √((0.34*(1-0.34))/1400)
CI = 0.34 ± 0.0295
CI = (0.3105, 0.3695)

Therefore, the answer is B, the 98% confidence interval of the proportion of American households who expect to buy a new car next year is (0.3105, 0.3695).