determine the null and alternative hypiotheses

Question

the max weights (in kilograms) for which one repetition of a half squat can be performed and the jump heights (in centimeters) for 12 soccer players are given in the accompanying table. r=0.780 at a=0.05, is there enough evidence to conclude that there is a significance linear correlation between the variables?

max weight  X        190  185  155   180  175  170  150   160  160  180  190  210        

jump height  Y       61   56  54  59  56  63  52  51  49  56  60  64

Determine the null and alternative hypotheses

Determine the critical value(s)

determine the standard test statistic

t=

Answer 1

There are 12 pairs of results, so there are 12-2=10 degrees of freedom. Using a=0.05 we see from the critical values table that the critical value of r is 0.576, but, since r=0.780, which is bigger than the critical value, there appears to be a correlation, and so the null hypothesis (that the results are due to chance) isn't valid (with a 95% chance of being correct about this). Therefore there appears to be a significant relationship to body weight and jump height (the alternative hypothesis).

Using the formula t=rsqrt((n-2)/(1-r^2))=0.780sqrt(10/(1-0.6084))=0.780sqrt(10/0.3916)=3.94. This value is higher than the 2.23 value in the t-test values table for a=0.05 and 10 degrees of freedom, so reinforces the hypothesis that there is a significant relationship between body weight and jump height.

 

Answer 2

H0:there is significant linear corelations btw the variables

H1;there is NO significant linear corelation btw the variables