Question

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Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed.

6 4 N 40 45 60 65 50 55 Mileage (in MPG)

a. We would like to use these data to evaluate the average gas mileage of all 2012 Prius drivers. Do you think this is reasonable? Why or why not?

b. The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for driverswho participate on fueleconomy.gov? Note any assumptions you must make as you proceed with the test.

c. ​​​​​​​​​​​​​​Calculate a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.

Answer 1

Answer: 14 users can drive Given that 2012 Toyota Prius Sample mean = 53-3mps Standard deviation = 5.2 mpc. 2 Yes, The mileage Of all 2020 a) average gas prius drives with pow we can rely this Sample unbaused Estimate of the population mean, However, the data has Some Extreme values as well. mean طعنامت

2 rided t-test with b) Somp gets 2012 prius. we need to perform one sample- hypothesis turting wing following asumptions 1) samples ose ird independent identical distribution 2) Sample follow nomal distributors MOLO Ho: mean - 50% Ho,i mean $50 (2 sided t-test) test statistic 1 te (533 - 50) std error standard Error 30, += (53.3 -50) vig = 3.3 3.741 -0.882 where as p-value 0.034. p-value > 0.05; thees at 55. level. Conclude that are reject Ho and an 150 mcan

Given that 95% Confidence interval apper limit: 56.302 lava lunit: 50.2976/ formola . *5.2 upper limit : 53.37 tcritical 714 laver linit 53.3 - teritical Vių tcritical et 0.05; 13 4 52 2.160