00:01
Hello students, given the values of x and y, from that we have computed summation of x, summation of y, summation of x square, summation of y square and summation of product of x and y.
00:14
Now in a part of the equation, here we have n is equal to 8.
00:20
The linear correlation coefficient is given by r is equal to n into summation of x y minus summation of x into summation of y divided by square root of n into summation of x square minus summation of x the whole square into square root of n into summation of y square minus summation of y the whole square.
00:51
Now substituting the values, we will get the value of correlation as 0 .9619.
01:00
To test whether there is a linear correlation between tar and nicotine, the null and alternative hypothesis are h naught t is equal to 0, there is no linear correlation h1 t not equal to 0.
01:26
The linear correlation coefficient is r is equal to 0 .9619 and n is equal to 8.
01:35
So, the test statistic is given by t is equal to r divided by square root of 1 minus r square divided by n minus 2.
01:49
Substituting the values, we will get the test statistic as 8 .6180.
01:56
Now the degrees of freedom is n minus 2 which is 6.
02:05
Here the critical value corresponding to the test statistic and degrees of freedom is 3 .707.
02:23
Here the test statistic is greater than tabled value 8 .6180 is greater than 3 .707.
02:43
Therefore, we reject the null hypothesis.
02:50
Now in b part of the question, coefficient of determination is given by r square is equal to 0 .9619 square is equal to 0 .9253...