An automatic merge system has been installed at the entrance ramp to a major highway. Prior to the installation of the system, investigators found the average stress level of drivers to be 8.2 on a 10-point scale. After installation, a sample of 50 drivers showed a mean stress level of 7.6 with a standard deviation of 1.8. Conduct a hypothesis test using a significance level of 0.01 to determine if the average stress at peak hours for drivers under the new system is less than 8.2.

The average stress at peak hours for drivers under the new system is not less than 8.2.

Step-by-step explanation:

In this case e need to determine whether the the average stress at peak hours for drivers under the new system is less than 8.2.

Prior to the installation of the automatic merge system, investigators found the average stress level of drivers to be 8.2 on a 10-point scale.

The hypothesis can be defined as follows:

H₀: The average stress at peak hours for drivers under the new system is not less than 8.2, i.e. μ ≥ 8.2.

Hₐ: The average stress at peak hours for drivers under the new system is less than 8.2, i.e. μ < 8.2.

The information provided is:

As the population standard deviation is not provided, we will use a t-test for single mean.

Compute the test statistic value as follows:

The test statistic value is -2.36.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the one-tailed t-test as follows:

*Use a t-table for the probability.

The p-value of the test is 0.011.

The p-value of the test is greater than the significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the average stress at peak hours for drivers under the new system is not less than 8.2.

the one on the bottom left

step-by-step explanation:

all of the other ones have a specific pattern

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!