Question

In a survey of 100 consumers, 60 stated that the next vehicle they purchase will be an electric vehicle.

Find a 99% confidence interval of the true % of consumers who plan to purchase an electrical vehicle next.
Multiple Choice
a. 53.7% to 66.3%
b. 51.9% to 68.1%
c. 50.4% to 69.6%
d. 47.4% to 72.6%

Answer 1

To find a 99% confidence interval for the true percentage of consumers who plan to purchase an electric vehicle next, we use the formula for the lower and upper bounds. Plugging in the values from the survey, the confidence interval is 53.7% to 66.3%.

Step-by-step explanation:

To find a 99% confidence interval for the true percentage of consumers who plan to purchase an electric vehicle next, we can use the formula:

Lower Bound = sample proportion - z * sqrt(sample proportion * (1 - sample proportion) / sample size)

Upper Bound = sample proportion + z * sqrt(sample proportion * (1 - sample proportion) / sample size)

Plugging in the values from the survey, where the sample proportion is 60% (0.60), the sample size is 100, and the z-value for a 99% confidence interval is approximately 2.576, we can calculate:

Lower Bound = 0.60 - 2.576 * sqrt(0.60 * (1 - 0.60) / 100)

Upper Bound = 0.60 + 2.576 * sqrt(0.60 * (1 - 0.60) / 100)

Simplifying the expressions:

Lower Bound = 0.537

Upper Bound = 0.663

Therefore, the 99% confidence interval of the true percentage of consumers who plan to purchase an electric vehicle next is 53.7% to 66.3%.