If everything else stays the same, the margin of error can be reduced by (select all that are true) :

a. increasing confidence level

b. decreasing sample size

c. increasing sample size

d. decreasing confidence level

c. increasing sample size

d. decreasing confidence level

Step-by-step explanation:

Formula for margin of error :

, = Population standard deviation.

, s= sample standard deviation.

, p= sample proportion.

Here z and t are critical values.

n= sample size.

Margin of error has critical t-value of z-value in the numerator .

⇒ Margin of error is proportional to the critical value.

⇒ Margin of error is proportional to the confidence level.

(The critical t-value of z-value is proportional the confidence level increases.)

So , Margin of error can be reduced by decreasing confidence level.

Also , Margin of error has square root of the sample size in the denominator.

⇒ Margin of error is inversely proportional to the sample size.

So , Margin of error can be reduced by increasing sample size.

Hence, the correct options area :

c. increasing sample size

d. decreasing confidence level

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'.