00:01
For this problem, we are told that, according to business professors, ta judge, and dm cable, tall people tend to earn more money over their career than short people earn.
00:11
Using data collected from participants in the national longitudinal surveys, the researchers computed the correlation between average earnings in dollars and height in inches for several occupations.
00:22
We're told that the results are given in the table shown below.
00:26
In part a, we are asked to interpret the value of r for people in...
00:30
In sales occupations.
00:32
So since we have that are greater than zero, that means that we have a positive, what we could say is a positive weekly linear correlation, which supports the hypothesis.
00:58
The fact that it supports the hypothesis, that is in an informal sense, but we would expect if the hypothesis is correct that there would be a positive correlation.
01:09
In part b, we are asked to compute r squared for people in sales occupations and to interpret the results.
01:15
So i'll just calculate that on screen.
01:18
0 .41 squared equals 0 .1681.
01:22
So that means that 16.
01:25
Actually, i'll type this out, so i don't have to scribble it down.
01:28
That implies that 16 .81 % of the variation in, what was the term, in earnings, can be explained by height.
01:46
So not all of it, but there is a positive correlation.
01:49
In part c, we are asked to give h -0 and h -a, the null and alternate hypotheses for testing whether average earnings and height are positively correlated.
01:58
So h -0 would be that row equals 0, and the alternate hypothesis would be that row is greater than 0, that there is a positive correlation.
02:13
In part d, we are asked to compute the test statistic for testing h0 and ha in part c for people in sales occupations.
02:21
So our test statistic here, tc, will be equal to r times the square root of n minus 2 divided by the square root of 1 minus r squared, which will then be equal to 0 .41 times the square root of 115 over the square root of 1 minus 0 .1681, which gives that tc will be equal to negative 25 .87...