Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U. S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

represent the sample mean

population mean

represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

The Confidence level is is 0.95 or 95%, the significance would be and , and we can calculate the critical value using the normal standard distribution and we got

And replacing we got:

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: