1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
3 years ago
11

Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline

that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same. Show your work.
Miles Per Gallon

Regular: Below Regular Premium Super Premium

$39.31 36.69 38.99 40.04

39.87 40.00 40.02 39.89

39.87 41.01 39.99 39.93

A.) 3.49
B.) 4.07
C.) 2.33
D.) 3.86
E.) 3.26

Mathematics
1 answer:
yawa3891 [41]3 years ago
3 0

Answer:

B) 4.07

Step-by-step explanation:

First we need to calculate the mean of all the data, which is the same as the mean of the means of each grade of gasoline:

Regular    BelowRegular   Premium   SuperPremium

39.31             36.69                38.99             40.04

39.87            40.00                40.02             39.89

39.87            41.01                  39.99             39.93

X1⁻=39.68    X2⁻= 39.23       X3⁻= 39.66    X4⁻=  39.95

Xgrand⁻ = (39.68+39.23+39.66+39.95)/4 = 39.63

Next we need to calculate the sum of squares within the group (SSW) and the sum of squares between the groups (SSB), and the respective degrees of freedom):

SSW = [ (39.31-39.68)² + (39.87-39.68)² + (39.87-39.68)² ] + [ (36.69-39.23)² + (40.00-39.23)² + (41.01-39.23)² ] + [ (38.99-39.66)² + (40.02-39.66)² + (39.99-39.66)² ] + [ (40.04-39.95)² + (39.89-39.95)² + (39.93-39.95)² ] = [0.2091] + [10.2129] + [0.6874] + [0.0121] = 11.12

SSW =  11.12

Degrees of freedom in this case is calculated by m(n-1), with m being the number of grades of gasoline (4) and n being the number of trial results for each one (3), so we would have 4(3-1) = 8 degrees of freedom

SSB = [ (39.68-39.63)² + (39.68-39.63)² + (39.68-39.63)²] + [ (39.23-39.63)² + (39.23-39.63)² + (39.23-39.63)² ] + [ (39.66-39.63)² + (39.66-39.63)² + (39.66-39.63)² ] + [ (39.95-39.63)² + (39.95-39.63)² +(39.95-39.63)² ] = [0.0075] + [0.48] + [0.0027] + [0.3072] = 0.7974

SSB =  0.80

For this case, the degrees of freedom are m-1, so we would have 4-1 = 3 degrees of freedom

Now we can establish the hypothesis for the test:

H0: μ1 = μ2 = μ3 = μ4

The null hypothesis states that the means of miles per gallon for each fuel are the same, indicating that the drade of gasoline does not make a difference, therefore our alternative hypothesis will be:

H1: the grade of gasoline does makes a difference

We will use the F statistic to test the hypothesis, which is calculated like follows:

F - statistic = (SSB/m-1) / (SSW/m(n-1)) = (0.80/3) / (11.12/8) = 0.19

We know that the level of significance we are using is α = 0.05, so to find the critical value F we need to look at some table of critical values for the F distribution for the 0.05 significance level (like the attached image). Then we just need to look fot the value that is located in the intersection between the degrees of freedom we have in the numerator (horizontal) and the denominator (vertical) of the statistic (3 and 8). That critical value is:

Fc = 4.07

You might be interested in
Paul wants to add new mulch to the top of all five garden beds. the new mulch will be 10 centimetres (cm) deep. about how much n
ladessa [460]
(4*4*10)*3
160*3=480
(5*3*10)*2
150*2=300
480+300=780 cub. meters
4 0
3 years ago
Read 2 more answers
(-2, 2), y=3x - 5 distance​
Andrews [41]

Answer:

If you are using slope intercept it is incorrect

Step-by-step explanation:

For the first part y is 2 so using y=Mx+b it’s 2=-6-5 which is not correct

7 0
3 years ago
In the figure below, abc is a right triangle. a + b = 150 degrees, and c + d = 35 degrees
timurjin [86]
Um i would need more details 
But i thing you would add those together
6 0
3 years ago
If x+3/3 = y+2/2, then x/3 = ______
timurjin [86]
X+1=y+1

X-Y= 0

Hope this helped you

7 0
2 years ago
9.54
damaskus [11]

Answer:

9.5

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Murphy and Naryam do their homework together. When they get to 9 - (-8) they get different answers. Murphy claims that the answe
    11·1 answer
  • Rearrange the formula A = πab 4 for b.
    10·2 answers
  • Alejandro has three ladders that are 15, 10, and 12 feet in length. If he is trying to reach a window that is 8 feet from the gr
    8·1 answer
  • I’m failing my math class and I need help with math because I don’t understand some stuff.
    12·2 answers
  • It is six o'clock in Germany. What time is it in New York?
    13·1 answer
  • P<br><img src="https://tex.z-dn.net/?f=p%202%20-%204p%20-%2012" id="TexFormula1" title="p 2 - 4p - 12" alt="p 2 - 4p - 12" align
    11·2 answers
  • What is the value of the expression, written in standard form?
    11·1 answer
  • Izzy manages the school baseball and softball teams. Part of his job is taking care of equipment and recording statistics about
    11·1 answer
  • More smart people pls
    15·2 answers
  • George is driving at an average speed of 707070 miles per hour. At this rate, how long, in minutes, will it take him to complete
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!