Question

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

Find a 90% 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

The 90% confidence interval for the true percentage of consumers who plan to purchase an electric vehicle next is approximately 51.9% to 68.1%.

Step-by-step explanation:

To find the 90% confidence interval for the true percentage of consumers who plan to purchase an electric vehicle, we use the formula for a confidence interval for a proportion:

Confidence Interval = p ± Z*(√(p(1-p)/n))

Where:

• p is the sample proportion, which is 60/100 = 0.6
• n is the sample size, which is 100
• Z* is the Z-value from the standard normal distribution corresponding to the desired confidence level. For a 90% confidence interval, Z* is approximately 1.645.

Plugging the values into the formula, we get:

Confidence Interval = 0.6 ± 1.645 * (√(0.6(1-0.6)/100))

Confidence Interval = 0.6 ± 1.645 * (√(0.24/100))

Confidence Interval = 0.6 ± 1.645 * (0.049)

Confidence Interval = 0.6 ± 0.080655

Confidence Interval = 0.519345 to 0.680655

Therefore, the 90% confidence interval for the proportion is approximately 51.9% to 68.1%.