Every user of statistics should understand the distinction between statistical significance and practical importance. a sufficiently large sample will declare very small effects statistically significant. let us suppose that sat mathematics (satm) scores in the absence of coaching vary normally with mean μ = 510 and σ = 90. suppose further that coaching may change μ but does not change σ. an increase in the satm score from 510 to 513 is of no importance in seeking admission to college, but this unimportant change can be statistically very significant. to see this, calculate the p-value for the test of the given hypotheses in each of the following situations.

hey there!

12 is twice as much as 6 because 6 goes into 12 2 times.

since the rabbit is twice as tall, we should multiply the weight of the first rabbit, 0.25, by 2.

0.25 x 2 = 0.5

therefore, the 12 inch chocolate rabbit weighs 0.5 lb, or half a pound.

hope this !

answer: -8.2562234e+13

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!