On average, Americans have lived in 4 places by the time they are 18 years old. Is this average a different number for college students? The 50 randomly selected college students who answered the survey question had lived in an average of 3.79 places by the time they were 18 years old. The standard deviation for the survey group was 1.2. What can be concluded at the α = 0.10 level of significance?

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is  no sufficient evidence to conclude that the average is a different number for college students

Step-by-step explanation:

From the question we are told that

    The  sample size is  n =  50  

    The  population mean is

     The  sample mean is

     The standard deviation is

     The  level of significance is  

The  null hypothesis is  

The alternative hypothesis is

Generally  the  test statistics is mathematically represented as

=>      

=>      

From the z table  the area under the normal curve to the left corresponding to    -1.237  is    

Generally the p-value is mathematically represented as

=>    

Generally  from the values obtained we see that

Hence

The decision rule is

Fail to reject the null hypothesis

 The conclusion is

There is  no sufficient evidence to conclude that the average is a different number for college students

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!

yes

step-by-step explanation: