<< Chapter < Page Chapter >> Page >
  • 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


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 t = r n 2 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: 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

the power of the test is
Ejaz Reply
bias came in sampling due to
Muzammil Reply
how do you find z if you only know the area of .0808
Cady Reply
construct a frequency distribution
How to take a random sample of 30 observations
Hamna Reply
you can use the random function to generate 30 numbers or observation
How we can calculate chi-square if observed x٫y٫z/frequency 40,30,20 Total/90
Insha Reply
calculate chi-square if observed x,y,z frequency 40,30,20total 90
find t value,if boysN1, ،32,M1,87.43 S1square,39.40.GirlsN2,34,M2,82.58S2square,40.80 Determine whether the results are significant or insignificant
The heights of a random sample of 100 entering HRM Freshman of a certain college is 157 cm with a standard deviation of 8cm. test the data against the claim that the overall height of all entering HRM students is 160 cm. previous studies showed that
Crispen Reply
complete the question.. as data given N = 100,mean= 157 cm, std dev = 8 cm..
Z=x-mu/ std dev
find the mean of 25,26,23,25,45,45,58,58,50,25
Asmat Reply
add all n divide by 10 i.e 38
1 . The “average increase” for all NASDAQ stocks is the:
Jamshaid Reply
STATISTICS IN PRACTICE: This is a group assignment that seeks to reveal students understanding of statistics in general and it’s practical usefulness. The following are the guidelines; 1.      Each group has to identify a natural process or activity and gather data about/from the process. 2.     
Kofi Reply
The diameter of an electric cable,say, X is assumed to be continoues random variable with p.d.f f(x)=6x(1-x); ≤x≤1 a)check that f(X) is p.d.f b) determine a number b such that p(Xb)
Syed Reply
A manufacturer estimate 3% of his output is defective. Find the probability that in a sample of 10 items (a) less than two will be defective (b) more than two will be defective.
A manufacturer estimates that 3% of his output of a small item is defective. Find the probabilities that in a sample of 10 items (a) less than two and (b) more than two items will be defective.
use binomial distribution with parameter n=10, p= 0.03, q=0.97
the standard deviation of a symmetrical distribution is 7.8 . what must be the value of forth moment about the mean in order that distribution be a) leptokurtic b) mesokurtic c) platy kyrtic intrept the obtain value of a b and c
Tushar Reply
A researcher observed that four out of every ten of their products are normally defective. A total of 360 samples of the products were being tested. If the sample is normally distributed and 220 of the products were identified to be faulty, test the hypothesis that the observation of the res
Adepoju Reply
please answer the ques"following values are obtained from life table T15=3,493,601 and e°15=44.6 then expected number of person alive at exact age 15 will be "
make it clear
how x minus x bar is equal to zero
Kashif Reply
When the mean (X bar) of the sample and the datapoint-in-context (X) from the same sample are the same, then it (X minus X bar) is equal to 0
e.g. mean of. sample is 3 and one of the datapoints in that sample is also 3
a numerical value used as a summary measure for a sample such as a sample mean is known as
rana Reply

Get the best Introductory statistics course in your pocket!

Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?