A researcher chooses a simple random sample of 100 Lexington, Kentucky, residents and finds that 20 of them have put in a reservation for a Tesla Model 3. A 95 percent confidence interval for the proportion of all Lexington, Kentucky, residents who have put in a reservation for that car is (approximately):
A) 20 ± 3.
B) 0.10 ± 0.04.
C) 0.95 ± 0.20.
D) 20 ± 6.
E) 0.20 ± 0.08.

Question

Quizplus · Accepted Answer

To find the confidence interval for the proportion of all Lexington, Kentucky residents who have put in a reservation for a Tesla Model 3, we can use the formula:

CI = p̂ ± z*sqrt((p̂(1-p̂))/n)

Where p̂ is the sample proportion, z is the critical value for the desired confidence level (95% in this case), and n is the sample size.

Plugging in the given values, we get:

CI = 0.2 ± 1.96*sqrt((0.2*(1-0.2))/100)
   = 0.2 ± 0.077

Rounding to two decimal places, we get the 95% confidence interval as (0.123, 0.277), which can be written as 0.20 ± 0.08. Therefore, the best choice is E.

A Researcher Chooses a Simple Random Sample of 100 Lexington