Question

Fill-Up No.	Computer	Driver	Difference
1	41.5	36.5	5
2	50.7	44.2	6.5
3	36.6	37.2	-0.6
4	37.3	35.6	1.7
5	34.2	30.5	3.7
6	45	40.5	4.5
7	48	40	8
8	43.2	41	2.2
9	47.7	42.8	4.9
10	42.2	39.2	3
11	43.2	38.8	4.4
12	44.6	44.5	0.1
13	48.4	45.4	3
14	46.4	45.3	1.1
15	46.8	45.7	1.1
16	39.2	34.2	5
17	37.3	35.2	2.1
18	43.5	39.8	3.7
19	44.3	44.9	-0.6
20	43.3	47.5	-4.2

QUESTION 1

1. Computers in some vehicles calculate various quantities related to car performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer-calculated mpg, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up.

   The data for a random sample of 20 of these the mpg values given in the csv file under variables Computer, Driver and Difference = (Computer – Driver).

   (Q1-9)Question: You suspect that that the car on-board-computer has been over-estimating the 41-mpg stated at the car-manufacturing website.

   Download the data file, Ch5_FuelEfficiency.csv, from Blackboard, and get the basic descriptive statistics for all three variables: Computer, Driver and Difference, using the following R codes:

   mydata <- read.csv("Ch5_FuelEfficiency.csv")

   #install.packages("pastecs")

   library(pastecs)

   stat.desc(mydata)

   The mean values for variables Computer, Driver and Differrence are 43.17, 40.44 and 2.73, respectively.

   Part I: Statistical inference for variable “Computer”

   1. Implement the hypothesis testing.

   a. State the hypotheses.

   Question 1: choose the right hypotheses for this problem.

   		H0: = =41   vs.    Ha: > 41
   		H0: = =41   vs.    Ha: ><41
   		H0: = =41   vs.    Ha:   ≠ 41
   		H0: = =43.17   vs.    Ha:   >43.17

2. QUESTION 2

3. b. Perform the test of significance using α = 5% and state/interpret your conclusion.

   Known:  n = 20, = 43.17 (Statistic), s = 4.41 (we use this as an estimate for σ)

   Question 2: What is the standard error?_________

   		4.41
   		3.5
   		3
   		0.9861

Answer 1

Note that at 5% level of significance we conclude that Reject null hypothesis. There is sufficient evidence from the given sample data that the average computer-recorded mpg measurement is larger than the stated 41 mpg.