A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows. Find the value of the F-test statistic for testing whether the average gas mileage is the same for the four car models. Round your answer to two decimal places, if necessary.

Car A Car B Car C Car D
Driver 1 23 39 22 25
Driver 2 37 39 28 39
Driver 3 39 40 21 25
Driver 4 34 36 27 33
Driver 5 27 35 26 37

Required:
Make the decision to reject or fail to reject the null hypothesis that there is no difference in the average gas mileages of the four car models. State the conclusion in terms of the original problem. Use alpha = 0.01.

a. We reject the null hypothesis. At the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models.
b. We fail to reject the null hypothesis. At the 0.01 level of significance, there is not sufficient evidence of a difference in average gas mileages of the four car models.
c. We fail to reject the null hypothesis. At the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models.
d. We reject the null hypothesis. At the 0.01 level of significance, there is not sufficient evidence of a difference in average gas mileages of the four car models.

We reject the null hypothesis at the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models  ( A )

Step-by-step explanation:

Using the Given data we will apply the two way ANOVA without

source of variation            SS             df        MS        F

Block                                  148.80       4        37.20    1.68

Treatment                         424.40       3        141.47     6.39

Error                                  265.60       12       22.13

Total                                  838.80       19

From the Two way ANOVA table the F-statistic = 6.39

300pi

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!