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. Using a = 0.05, is there sufficient evidence to conclude that the proportion of Americans who purchased an electric car is different from 0.2? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document.

1. Define the population parameter in one sentence.
2. State the null and alternative hypotheses using correct notation.
3. State the significance level for this problem.
4. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round during the calculation. Then, round the test statistic to two decimal places after you complete the calculation.
5. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value.
6. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this).
7. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

Use StatCrunch (Stat → Proportion Stats → One Sample → with Summary) to verify your test statistic and p-value. Copy and paste this box into your document.

Answer 1

Hence we conclude that there sufficient evidence to conclude that the proportion of Americans who purchased an electric car is different from 0.2