The difference between teenage female and male depression rates estimated from two samples is 0.08. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval? Use the critical value z = 1.96.

= ( 0.0384, 0.1216)

Therefore at 95% confidence interval the difference between teenage female and male depression rates is between ( 0.0384, 0.1216)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 0.08

Standard deviation r = 0.03

Number of samples n = 2

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

0.08+/-1.96(0.03/√2)

0.08+/-1.96(0.021213203435)

0.08+/-0.0416

= ( 0.0384, 0.1216)

Therefore at 95% confidence interval= ( 0.0384, 0.1216)

73.0769230769% of the games were won

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!