Question

As a procrastination activity, you have been observing students scaling

the climbing wall and have been tracking the success of these students at

reaching the top of the wall as a function of their sex. Of 20 women you

observed 16 reached the top successfully and of 30 men you observed, 14

reached the top successfully. Based on these data, is there a significant

( < : 05) relationship between sex and climbing success? Of what

magnitude is the relationship?

(HINT: Its Chi-sq problem)

Answer 1

Table of observed frequencies (O_ij) is given as follows:

	Male	Female	Total
Top	14	16	30
Bottom	16	4	20
Total	30	20	50

Table of expected frequencies (E_ij) is given as follows:

E_ij=Sum of ith column* Sum of jth column/N

	Male	Female	Total
Top	18	12	30
Bottom	12	8	20
Total	30	20	50

We have to test here

H0: There is no relationship between Sex and climbing success.

Vs

H1:There is relationship between Sex and climbing success.

Test statistic for testing above hypothesis is,

T=(O_ij-E_ij)²/E_ij=(14-18)²/18 +(16-12)²/12 +(16-12)²/12 +(4-8)²/8 =5.555556

Critical value=_0.05,1=3.841459

Since, T>_0.05,1=3.841459, we reject H0 at 5% level of significance and conclude that there is relationship between Sex and

climbing success.