Null Hypothesis
H
0 : The population correlation coefficient IS NOT significantly different from zero. 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 zero. There IS A SIGNIFICANT LINEAR RELATIONSHIP (correlation) between
x and
y in the population.
Drawing a conclusion:
There are two methods of making the decision. The two 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%,
α = 0.05
Note
Using the
p -value method, you could choose any appropriate significance level you want; you are not limited to using
α = 0.05. But the table of critical values provided in this textbook assumes that we are using a significance level of 5%,
α = 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
To calculate the
p -value using LinRegTTEST:
On the LinRegTTEST input screen, on the line prompt for
β or
ρ , 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 zero."
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 zero."
Calculation notes:
You will use technology to calculate the
p -value. The following describes the calculations to compute the test statistics and the
p -value:
The
p -value is calculated using a
t -distribution with
n - 2 degrees of freedom.
The formula for the test statistic is
. 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.
The line of best fit is: ŷ = -173.51 + 4.83
x with
r = 0.6631 and there are
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)?
H
0 :
ρ = 0
H
a :
ρ ≠ 0
α = 0.05
The
p -value is 0.026 (from LinRegTTest on your calculator or from computer software).
The
p -value, 0.026, is less than the significance level of
α = 0.05.
Decision: Reject the Null Hypothesis
H
0
Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (
x ) and the final exam score (
y ) because the correlation coefficient is significantly different from zero.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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