



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 pvalue

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 pvalue 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 pvalue to make a decision
 The linear regression
$t$ test LinRegTTEST on the TI83+ or TI84+ calculators calculates the pvalue.
 On the LinRegTTEST input screen, on the line prompt for
$\beta $ or
$\rho $ , highlight "
≠ 0 "
 The output screen shows the pvalue on the line that reads "p =".
 (Most computer statistical software can calculate the pvalue.)
If the pvalue 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 pvalue 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 pvalue. The following describe the calculations to compute the test statistics and the pvalue:
 The pvalue is calculated using a
$t$ distribution with
$\mathrm{n2}$ degrees of freedom.
 The formula for the test statistic is
t=\frac{r\sqrt{n2}}{\sqrt{1r^{2}}} . The value of the test statistic,
$t$ , is shown in the computer or calculator output along with the pvalue. The test statistic
$t$ has the same sign as the correlation coefficient
$r$ .
 The pvalue is the combined area in both tails.
 An alternative way to calculate the pvalue
(p) given by LinRegTTest is the command 2*tcdf(abs(t),10^99, n2) 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:
$\hat{y}=173.51+\text{4.83x}$ 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)?
Questions & Answers
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
ninjadapaul
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X6)^2
so it's 20 divided by X6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
if A not equal to 0 and order of A is n prove that adj (adj A = A
rolling four fair dice and getting an even number an all four dice
Differences Between Laspeyres and Paasche Indices
No. 7x 4y is simplified from 4x + (3y + 3x) 7y
J, combine like terms 7x4y
im not good at math so would this help me
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)1/7 (x1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials and their applications of sensors.
what is system testing?
AMJAD
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field .
1Electronicsmanufacturad IC ,RAM,MRAM,solar panel etc
2Helth and MedicalNanomedicine,Drug Dilivery for cancer treatment etc
3 Atomobile MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Quantitative information analysis iii. OpenStax CNX. Dec 25, 2009 Download for free at http://cnx.org/content/col11155/1.1
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