Question

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency. For one vehicle equipped in this way, the number of ‘liters per 100 kilometers’ driven were recorded each time the gas tank was filled, and the computer was then reset. Below are the ‘liters per 100 kilometers’ driven for a random sample of 20 of these records. 5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3, 4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4. Calculate a 95% confidence interval for the average liters per 100 kilometres for this vehicle. Use RStudio or R on Jupyter in order to solve this problem.

Provide all your work with your solutions. Is the CI you obtained valid? In order to answer this question, • List all assumptions required. • For each assumption, indicate whether it holds and why it does or does not. • When appropriate, provide graphical displays in order to assess a particular assumption. • Explain how based on such graphs, you decided whether the corresponding assumption seems to hold or not.

Answer 1

Answer:

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency. For one vehicle equipped in this way, the number of ‘liters per 100 kilometers’ driven were recorded each time the gas tank was filled, and the computer was then reset. Below are the ‘liters per 100 kilometers’ driven for a random sample of 20 of these records. 5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3, 4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4. Calculate a 95% confidence interval for the average liters per 100 kilometres for this vehicle. Use RStudio or R on Jupyter in order to solve this problem.

Provide all your work with your solutions. Is the CI you obtained valid? In order to answer this question, • List all assumptions required. • For each assumption, indicate whether it holds and why it does or does not. • When appropriate, provide graphical displays in order to assess a particular assumption. • Explain how based on such graphs, you decided whether the corresponding assumption seems to hold or not.

Result:

95% CI = (5.218781, 5.781219)

shapiro.test value W = 0.92693, p-value = 0.1347 which is > 0.05 level of significance. The data not violate the normal assumption.

data plot shows the data are approximately normally distributed.

R code:

time=c(5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3, 4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4)

shapiro.test(time)

qqnorm(time)

qqline(time)

library(Rmisc)

CI(time,ci=0.95)  

Output:

CI(time,ci=0.95)

   upper     mean    lower 

5.781219 5.500000 5.218781 

shapiro.test(time)

        Shapiro-Wilk normality test

data:  time

W = 0.92693, p-value = 0.1347