# 11.3 Test of independence  (Page 3/20)

 Page 3 / 20

De Anza College is interested in the relationship between anxiety level and the need to succeed in school. A random sample of 400 students took a test that measured anxiety level and need to succeed in school. [link] shows the results. De Anza College wants to know if anxiety level and need to succeed in school are independent events.

Need to succeed in school vs. anxiety level
Need to Succeed in School High
Anxiety
Med-high
Anxiety
Medium
Anxiety
Med-low
Anxiety
Low
Anxiety
Row Total
High Need 35 42 53 15 10 155
Medium Need 18 48 63 33 31 193
Low Need 4 5 11 15 17 52
Column Total 57 95 127 63 58 400

a. How many high anxiety level students are expected to have a high need to succeed in school?

a. The column total for a high anxiety level is 57. The row total for high need to succeed in school is 155. The sample size or total surveyed is 400.

$E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}=\frac{155\cdot 57}{400}=22.09$

The expected number of students who have a high anxiety level and a high need to succeed in school is about 22.

b. If the two variables are independent, how many students do you expect to have a low need to succeed in school and a med-low level of anxiety?

b. The column total for a med-low anxiety level is 63. The row total for a low need to succeed in school is 52. The sample size or total surveyed is 400.

c. $E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}$ = ________

c. $E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}=8.19$

d. The expected number of students who have a med-low anxiety level and a low need to succeed in school is about ________.

d. 8

## Try it

Refer back to the information in [link] . How many service providing jobs are there expected to be in 2020? How many nonagriculture wage and salary jobs are there expected to be in 2020?

12,727, 14,965

## References

DiCamilo, Mark, Mervin Field, “Most Californians See a Direct Linkage between Obesity and Sugary Sodas. Two in Three Voters Support Taxing Sugar-Sweetened Beverages If Proceeds are Tied to Improving School Nutrition and Physical Activity Programs.” The Field Poll, released Feb. 14, 2013. Available online at http://field.com/fieldpollonline/subscribers/Rls2436.pdf (accessed May 24, 2013).

Harris Interactive, “Favorite Flavor of Ice Cream.” Available online at http://www.statisticbrain.com/favorite-flavor-of-ice-cream (accessed May 24, 2013)

“Youngest Online Entrepreneurs List.” Available online at http://www.statisticbrain.com/youngest-online-entrepreneur-list (accessed May 24, 2013).

## Chapter review

To assess whether two factors are independent or not, you can apply the test of independence that uses the chi-square distribution. The null hypothesis for this test states that the two factors are independent. The test compares observed values to expected values. The test is right-tailed. Each observation or cell category must have an expected value of at least 5.

## Test of independence

• The number of degrees of freedom is equal to (number of columns - 1)(number of rows - 1).
• The test statistic is $\underset{\left(i\cdot j\right)}{\Sigma }\frac{{\left(O–E\right)}^{2}}{E}$ where O = observed values, E = expected values, i = the number of rows in the table, and j = the number of columns in the table.
• If the null hypothesis is true, the expected number $E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}$ .

what is permutation
how to construct a histogram
I really appreciate that
I want to test linear regression data such as maintenance fees vs house size. Can I use R square, F test to test the relationship? Is the good condition of R square greater than 0.5
yes of course must have use f test and also use t test individually multple coefficients
rishi
Alright
umar
hi frnd I'm akeem by name, I wanna study economics and statistics wat ar d thing I must do to b a great economist
akeem
Is R square cannot analysis linear regression of X vs Y relationship?
Mok
To be an economist you have to be professional in maths
umar
hi frnds
Shehu
what is random sampling what is sample error
@Nistha Kashyap Random sampling is the selection of random items (or random numbers) from the group. A sample error occurs when the selected samples do not truely represent the whole group. The can happen when most or all of the selected samples are taken from only one section of the group;
Ron
Thus the sample is not truely random.
Ron
What is zero sum game?
A game in which there is no profit & no loss to any of the both player.
Milan
Differences between sample mean & population mean
***keydifferences.com/difference-between-sample-mean-and-population-mean.html
Lucien
Not difference in the formula except the notation, sample mean is denoted by x bar and population mean is denoted by mu symbol. There is formula as well as notation between difference variance and standard deviations
Akash
Likely the difference would be in the result, unless the sample is an exact representation of the population (which is unlikely.)
Ron
what is data
Nii
Nii Avin - Data is just a simple way to refer to the numbers in the population, or in the sample used in your calculations.
Ron
what are the types of data
Nii
Data is the very pale android from the Star Trek Enterprise
Andrew
Am Emmanuel from Nigeria
Emmanuel
Am Qudus from Nigeria
Rasak
am Handson from Cameroon
Handson
what is a mode?
Handson
Nii - data is whatever you are sampling. Such as the number of students in each classroom.
Ron
Handson Ndintek - the mode is the number appearing most frequently. Example: 7 9 11 7 4 6 3 7 2. 7 is the mode. In a group such as 7 9 1 4 6 3, there is no mode because no number appears more often than any other.
Ron
hi I want to know how to find class boundary
Baalisi
give me the two types of data
qualitative and quantitative
phoenix
primary and secondary data
Peace
qualitative and quantitative
Prince
Using Cauchy Schwartz inequality,or prove that b2-b1-1=0
what is the ongoing probability that President Trump will remain in the position he has chosen as his viability of his cabinet as he runs for reelection in the primaries of 2020 election year
Terry
what is statistic?
it's a science of collection, organization, analysis and summarizing data to get useful information to make several types of conclusions.which can be used in real life.
anshika
what is the statistical probability that president Trump will remain in the white house after the election of 2020?
Terry
i agree with anshika is right but let me add that such decisions are made in face of uncertainty
Maureen
yes
Stephen
classification of statistic
statistic can classified into many types eassy to understand future values effect
Narendra
what is mean?
Jhasaketan
average value
Narendra
İ want to understand what is t test or neyma. Pearson test ans difference
Yasin
to test the hypotesis ho follws h1 l1/lo
Narendra
Hope this helps. There are three main types of averages. *mean -> average -> (X1+X2+X3+...+Xn) / n *mode -> the element within a set which occurs most. {3,4,5,8,12,3,4,3,3,56} mode = 3 *median -  {3,3,4,5,8,12,56} median = 5 OR {3,4,5,8,12,56} median = 6.5
Jack
conceptual approach to limits
how are limits derived?
lameck
an entire section of calculus is devoted to that explanation.
Pitior
what is statistics?
statistics :- can be defined as the branches of mathematics that deals with the summarizing, analysing,organization and interpretation of data.
Usman
well said
Venkat
can we find Z value on calculator with out using Z table
no
Pitior
why
Maham
can another way is possible ?
Maham
Well you could make a table. And as the function you use the one used at the z table
Luca
The normal function is only one way, so you can only try using different numbers until you get the probability that you have. So that is easier if you have a table
Luca
me don't know nothing about z table and don't know how to see the z value on table can you tell me please how see the value on table
Maham
The z table is the table of the standard normal distribution
Luca
You can look it up on internet, its easier than writing down the normal distribution function (with an integral) and doing a table in the calculator
Luca
OK thanks luca
Maham
yes use pnorm in r
Venkat
pnorm(2.3,mean=0,sd=1)
Venkat
pnorm?
Maham
do u have r software
Venkat
no
Maham
its with tht u will get
Venkat
Venkat
z mathportal calculator
Venkat
calculator
Venkat
OK venkat thanks
Maham
welcome
Venkat
have calculator but don't know how find z value
Maham
ti83
Venkat
hey guys I'm from computer background so what are the concepts I supposed to prepare for interview in statistics
Alwin
descriptive stats
Venkat
inferential stats
Venkat
outlier treatment
Venkat
boxplot
Venkat
ok
Alwin
assumption of linear regression
Venkat
logistic regression
Venkat
k means clustering
Venkat
exact syllabus?
Alwin
type. analytics vidya interview questions statistics
Venkat
listen. data also
Venkat
like this forum
Jameel
My question is "is it only stats?"
Jameel
wer is the problem
Venkat
how find straight line equation in regression
u can find using excel
Venkat
or r studio
Venkat
for regression
Venkat
shall i help
Venkat
im an expert
Venkat
by giving a value to x,y
Ibrokhim
first provide data
Venkat
ill solve and guve
Venkat
ive
Venkat
Maham
maham you posted data
Venkat
Venkat
ok
Maham
x:1,2,3,4,5 y:2,5,6,8,9
Maham
regredsion equation is
Venkat
y=0.9+1.7x
Venkat
reg eq is y=0.9+1.7x
Venkat
slope = 1.7
Venkat
yintercept = 0.9
Venkat
Venkat
thanx venkat naveen😊
Maham
welcome
Venkat