An automobile manufacturer has given its jeep a 50.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 280 jeeps, they found a mean MPG of 50.7. Assume the population standard deviation is known to be 1.3. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is different from 50.5 mpg

Step-by-step explanation:

Data given and notation  

represent the sample  mean

represent the population standard deviation for the sample  

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

Sytem of hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 50.5, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Replacing we got:  

P-value

Since is a two tailed test the p value would be:  

Conclusion  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is different from 50.5 mpg

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!