Assume a significance level of

α=0.05

and use the given information to complete parts (a) and (b) below. original claim:

lessless

than

51%

of adults would erase all of their personal information online if they could. the hypothesis test results in a p-value of

0.0148

a. state a conclusion about the null hypothesis. (reject

upper h 0h0

or fail to reject

upper h 0h0.)

choose the correct answer below.

a.

rejectreject

upper h 0h0

because the p-value is

less than or equal toless than or equal to

alphaα.

b.

rejectreject

upper h 0h0

because the p-value is

greater thangreater than

alphaα.

c.

fail to rejectfail to reject

upper h 0h0

because the p-value is

greater thangreater than

alphaα.

d.

fail to rejectfail to reject

upper h 0h0

because the p-value is

less than or equal toless than or equal to

alphaα.

b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion?

a.

the percentage of adults that would erase all of their personal information online if they could is

lessless

than or equal to

51%.

b.

there

isis

sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

c.

the percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

d.

there

is notis not

sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is

moremore

than

51%.

Part a: The correct answer is A, reject H0 because p value is less than . Part B: The correct answer is C, the percentage of adults that would erase their personal information online if they could is more than 51%.

Step-by-step explanation:

part a. The essential idea of hypothesis testing in statistics is to evaluate the probability p (p value) of some representative parameter, compared to a level of likelihood that is set before starting the test (). In this case, we are interested in a level of likelihood , which means that if the probability of the parameter is less than 5%, we will reject the hypothesis that this parameter is representing, since it's so unlikely. Of course, the significance level is arbitrary and must be payed attention, according to the particular situation. Therefore, the correct anser is A.

part b. Since we rejected the hypothesis to a 5% significance level, we reject the fact that less than 51% of adults would erase their personal information online if they could. This is equivalent to saying that a percentage of adults equal to or more than 51% would erase their personal information if they could, which is answer C.

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!