Heather is a student in a class that has been asked to conduct a hypothesis test for a population proportion. the null and alternative hypotheses are: h0: p = 0.5 ha: p ≠ 0.5 heather is given a sample and calculates the test statistic. using a level of significance of α = 0.05, she rejects the null hypothesis. heather's friends, alan and bill, also use the sample to calculate a test statistic. however, they differ in the level of significance they use. alan uses a level of significance of α = 0.1, while bill uses α = 0.01. all three students perform their calculations correctly. for each of heather's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given.

Alan = reject H0

Bill = cannot say

Step-by-step explanation:

Given that Heather is a student in a class that has been asked to conduct a hypothesis test for a population proportion.

(two tailed test at 5% significance level)

Since she rejects null hypothesis p value should have been less than 0.05

when p value <0.05, it is definitely less than 0.10

So at 1% level of significance also the null hypothesis would be rejected.

So Alan also would get the same result as to reject the H0

But about Bill since Bill uses 0.01, we cannot definitely say that p value is less than or greater than 0.01

All we know is that p is less than 0.05

Hence it is impossible to tell from the information for Bill

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!