An automobile manufacturer wants to assess a new style of visual display to see if it changes the amount of reported eye-strain among long-distance drivers. In the study, sixteen people use a driving simulator with the standard display, and later, the same sixteen people use the simulator again, but this time the new style of display is present. The dependent variable is the reported eye strain, reported on a scale of 1 (extreme strain) to 15 (no eye strain). Does the new display differ in terms of reported eye strain? d = New style-old style mean difference = 3.8 standard deviation of the difference scores - 1.36. Using the information above, perform the appropriate test with alpha - .05 and match the statistics below with the correct value. Be sure to round the standard error to two decimal places in the calculation.
Premise Response
standard error = A 3.15
t-statistic → = B 7.20
= C 11.18
= D .95
= E 11.38

Standard error = 0.34

t-statistic = 11.18

Step-by-step explanation:

Given Data:

Mean difference d = 3.8

Standard deviation S.D = 1.36

Number of people = 16

The appropriate test are:

1. Standard error

2. T- statistic

1. Calculating the standard error using the formula;

Standard error = S.D/√n

                         = 1.36/√16

                          = 1.36/4

                           = 0.34

2. Calculating the t-statistic using the formula;

t-statistic = d/(S.D/√n)

              = 3.8/(1.36/√16)

              = 3.8/(1.36/4)

              = 3.8/0.34

               = 11.18

This equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Note that parallel lines have the same slope.

The equation is y = 2x - 1; the slope is 2 and the y-intercept is (0, -1).

For our line parallel to the given line, we have y = 2x + b, as the slopes are the same. To find b (the y-intercept), plug the point on the line - (4, 2) - for x and y in the equation and solve algebraically for b.

y = 2x + b

2 = 2(4) + b

2 = 8 + b

-6 = b

We can now complete our equation!

y = 2x - 6

However, notice how the options aren't in slope-intercept form. Simply isolate and negate the constant to figure out which one is correct.

y = 2x - 6

y - 2x = -6

-y + 2x = 6

2x - y = 6

The equation of the line that passes through (4, 2) and is parallel to the line y = 2x - 1 is B) 2x - y = 6.