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.

e. Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test and connect it to the confidence interval you constructed in part (b)). Answer this question in one to two sentences.

Answer 1

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.

One sample proportion test

Test proportion is 1 in 5 or 1/5 = 0.2

Ho: P=0.2, H₁: P≠0.2

Sample proportion p=80/285 =0.2807

=3.406

Table value of z at 0.05 level = 1.96

Rejection Region: Reject Ho if z < -1.96 or z > 1.96

Calculated z = 3.406 , falls in the rejection region

The null hypothesis is rejected.

e. Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test and connect it to the confidence interval you constructed in part (b)). Answer this question in one to two sentences.

There is close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values in the interval are considered plausible values for the population proportion being estimated. When the null hypothesis is rejected, we are 95% confident that population proportion is not contained in the interval. In our problem, 95% confidence inter for the proportion is (0.2285, 0.3329). The null hypothesis proportion 0.2 is outside the 95% CI. There fore we reject the null hypothesis. Both hypothesis test and confidence interval produces the same result.