The number of shots taken and points scored by 8 players in a basketball game are shown in the table. Number of shots taken 1 4 7 8 10 11 11 14
Number of points scored 0 4 8 9 14 12 15 22

A basketball coach is investigating whether the number of shots taken can be used to predict the mean number of points scored. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in the number of points scored for each increase of 1 shot taken?

a. A one-sample t-interval for means.
b. A linear regression t-interval for slope.
с. A two-sample t-interval for a difference between means.
d. A matched-pairs t-interval for a mean difference.
e. A two-sample z-interval for a difference between proportions

d. A matched-pairs t-interval for a mean difference.

Step-by-step explanation:

d. A matched-pairs t-interval for a mean difference.

There are many situations in which two samples are not independent. This happens when the observations are found as pairs and the observations are related in pairs.

When the observations from two samples are paired either naturally or by design , the difference between two observation of each pair is treated as normal population  with mean ud= u1=u2  and unknown standard deviation, one sample t- test can be performed on them.

This is called matched pairs t- interval for a mean difference.

In this experiment the basketball coach is investigating whether the number of shots taken can be used to predict the mean number of points scored.

We want to estimate the mean change in the number of points scored for each increase of 1 shot taken.

The two samples are not independent.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.