The speeds (in km/h) of a sample of 27 vehicles travelling on a highway are meas

Question

The speeds (in km/h) of a sample of 27 vehicles travelling on a highway are measured, and the ages of the drivers are recorded. The sample correlation between the age of a driver and the speed of their vehicle is calculated to be -0.447.  

We would like to conduct a hypothesis test for correlation at the 5% level of significance to determine whether a linear relationship exists between the age of drivers and the speed they drive.

(a) What are the hypotheses for the appropriate test of significance?

(b) What is the test statistic for the appropriate test of significance?

(c) What is the P-value of the test?

(d) What is the correct conclusion for the test?

(e) Suppose we had instead conducted the test using the critical value method. What would be the decision rule and the conclusion?

Explanation / Answer

a) Ho : rho = 0   H1 : rho is differen from 0

t = -0.447 * 25   / srqt ( 1 - 0.447^2 )

t = -12.49

since t value is lower ( very lower ) p value is 0.00000001

conclusion there is a relationship between variables

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