A sample of data from 40 households in a particular area in 2007 yielded the following information, where X is disposeable income per head and Y is disposeable expenditure per head.

I am asked to show that the nul hypothesis will not be rejected against either a one or two tailed test.

This is what i have so far, but i think i might have got lost a little bit along the way ! Hopefully someone can point me in the right direction, thanks.

Significence level is 5 %

For my critical value i will use the t statistic with n - 2 degress of freedom, so for the one tailed test, t = 1.684, two-tailed, t = 2.021. (my statistical table dont give the value for 38 so i have used the value for 40.)

Calculate test statistic

Where

Where

Solving these gives

I reach this point and then i guess i have to compare the t score with some value to see if it is rejected or not ?