Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5.9 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 24 samples is 5.6 ppm with a standard deviation of 1.0. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to three decimal places.

t = -0.061

Step-by-step explanation:

We are given;

Population mean; μ = 5.9

Sample mean; x¯ = 5.6

Sample size; n = 24

standard deviation; σ = 1

Significance level = 0.02

Formula for the test statistic since sample size is less than 30 is;

t = (x¯ - μ)/(σ/√n)

t = (5.6 - 5.9)/(1/√24)

t = -0.3/(1/√24)

t = -0.061

3432532

step-by-step explanation:

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!