# 12.6 Testing the significance of the correlation coefficient  (Page 2/3)

 Page 2 / 3

## Setting up the hypotheses:

• Null Hypothesis: ${H}_{o}$ : $\rho$ = 0
• Alternate Hypothesis: ${H}_{a}$ : $\rho$ ≠ 0

## What the hypotheses mean in words:

• Null Hypothesis ${H}_{o}$ : The population correlation coefficient IS NOT significantly different from 0. There IS NOT a significant linear relationship(correlation) between $x$ and $y$ in the population.
• Alternate Hypothesis ${H}_{a}$ : The population correlation coefficient IS significantly DIFFERENT FROM 0. There IS A SIGNIFICANT LINEAR RELATIONSHIP (correlation) between $x$ and $y$ in the population.

## Drawing a conclusion:

• There are two methods to make the decision. Both methods are equivalent and give the same result.
• Method 1: Using the p-value
• Method 2: Using a table of critical values
• In this chapter of this textbook, we will always use a significance level of 5%, $\alpha$ = 0.05
• Note: Using the p-value method, you could choose any appropriate significance level you want; you are not limited to using $\alpha$ = 0.05. But the table of critical values provided in this textbook assumes that we are using a significance level of 5%, $\alpha$ = 0.05. (If we wanted to use a different significance level than 5% with the critical value method, we would need different tables of critical values that are not provided in this textbook.)

## Method 1: using a p-value to make a decision

• The linear regression $t$ -test LinRegTTEST on the TI-83+ or TI-84+ calculators calculates the p-value.
• On the LinRegTTEST input screen, on the line prompt for $\beta$ or $\rho$ , highlight " ≠ 0 "
• The output screen shows the p-value on the line that reads "p =".
• (Most computer statistical software can calculate the p-value.)

## If the p-value is less than the significance level (α = 0.05):

• Decision: REJECT the null hypothesis.
• Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between $x$ and $y$ because the correlation coefficient is significantly different from 0."

## If the p-value is not less than the significance level (α = 0.05)

• Decision: DO NOT REJECT the null hypothesis.
• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between $x$ and $y$ because the correlation coefficient is NOT significantly different from 0."

## Calculation notes:

• You will use technology to calculate the p-value. The following describe the calculations to compute the test statistics and the p-value:
• The p-value is calculated using a $t$ -distribution with $\mathrm{n-2}$ degrees of freedom.
• The formula for the test statistic is $t=\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}$ . The value of the test statistic, $t$ , is shown in the computer or calculator output along with the p-value. The test statistic $t$ has the same sign as the correlation coefficient $r$ .
• The p-value is the combined area in both tails.
• An alternative way to calculate the p-value (p) given by LinRegTTest is the command 2*tcdf(abs(t),10^99, n-2) in 2nd DISTR.

## Third exam vs final exam example: p value method

• Consider the third exam/final exam example .
• The line of best fit is: $\stackrel{^}{y}=-173.51+\text{4.83x}$ with $r=0.6631$ and there are $\mathrm{n = 11}$ data points.
• Can the regression line be used for prediction? Given a third exam score ( $x$ value), can we use the line to predict the final exam score (predicted $y$ value)?

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.