Question

Problem 3: Electric Cars (No StatCrunch Data Set)

According to both a Consumer Report’s and a AAA survey, about 1 in 5 Americans will buy an electric car as their next vehicle. To test this claim, an independent surveyor obtained records for 2018 car sales. The surveyor generated a random sample of 285 car sales and found that 80 of these new car purchases were of electric cars.  

1. Check the three conditions of the Central Limit Theorem that allow you to use the One-Proportion Confidence Interval using one complete sentence for each condition. Show work for the numerical calculation.

b. Construct a 95% confidence interval to estimate the population proportion of Americans new car purchases that were electric. Calculate this “by hand” using the formula and showing your work (please type your work, no images accepted here). Round your confidence limits to four decimals.

c. Verify your result in part (a) using Stat → Proportions Stats → One Sample → With Summary. Copy and paste your StatCrunch result in your document as well.

Answer 1

Check the three conditions of the Central Limit Theorem that allow you to use the One-Proportion Confidence Interval using one complete sentence for each condition. Show work for the numerical calculation.

Conditions

1. Each sample should represent a random sample from the population or at least follow the population distribution.

2. The sample size must not be bigger than 10% of the entire population.

3 Sample size n should be large enough so that np>=10 and nq>=10

n = 285

p = 80/285 = 0.28

q = 0.72

np = 285*0.28 = 80 which is greater than 10

nq = 28*072 = 205 which is greater than 10

b. Construct a 95% confidence interval to estimate the population proportion of Americans new car purchases that were electric. Calculate this “by hand” using the formula and showing your work