An athletic trainer wants to find out if there is a significant difference in the mean height of football players and basketball players in a large school district. She randomly selects 100 high school varsity football players and 100 high school varsity basketball players to compare the mean heights for each group.
1. Which of the following is the most appropriate statistical test to use to determine if there is a significant difference in mean height between basketball and football players?
A) ANOVA
B) Chi-squared test for independence
C) Matched pairs t-test
D) Inference for regression
E) Two-sample t-test

A) ANOVA

Step-by-step explanation:

Analysis of Variance is a statistical method invented by Ronald Fisher. This statistical method is employed in the analysis of the difference between the mean of two groups in a sample. We have the one-way and the two-way ANOVA tests.

The one-way ANOVA test has one independent variable, whereas, the two-way ANOVA test has two independent variables. The example of the athletic trainer is that of a one-way ANOVA test as it examines the difference in only the mean height of the players.

The ANOVA test is useful in determining if the result of a study is statistically significant. It also tells the researcher if he is to accept or reject either the null or alternate hypotheses.

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!