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 90% confidence interval of the proportion of American households who expect to buy a new car next year.

Question

Quizplus · Accepted Answer

To construct the confidence interval, we can use the formula:
Margin of error = z*sqrt((p̂*(1-p̂))/n)
where z is the z-score for the desired confidence level (90% corresponds to a z-score of 1.645), p̂ is the sample proportion (0.34), and n is the sample size (1400).
Plugging in the values, we get:
Margin of error = 1.645*sqrt((0.34*(1-0.34))/1400) = 0.0209
To find the lower and upper bounds of the interval, we can subtract and add the margin of error to the sample proportion:
Lower bound = 0.34 - 0.0209 = 0.3191
Upper bound = 0.34 + 0.0209 = 0.3609
Thus, the 90% confidence interval is [0.3191, 0.3609], which corresponds to choice B.