Question

 

Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

	Left-Handed	Right-Handed
Men	13	22
Women	27	18

Answer 1

H0: Null hypothesis: There is no relationship between handedness and gender

HA: Alternative hypothesis: There is relationship between handedness and gender.

Observed frequencies

                     Left handed         Right handed             Total

Men                    13                     22                         35

Women              27                      18                       45

Total                  40                     40                         80

Assuming H0, the expected frequencies are obtaind as follows:

              Left handed             Right handed              Total

Men       40X35/80=17.5              17.5                       35

Women      22.5                         22.5                       45

O              E                      O - E                     (O - E)²             (O -E)²/E

13          17.5                    - 4.5                        20.25              1.1571

22           17.5                     4.5                        20.25              1.1571

27           22.5                  4.5                        20.25                   0.9

18          22.5                  - 4.5                        20.25                 0.9

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                                                                                  = 4.1142

ndf = 4 - 1 = 3

= 0.05

From Table, critical value of = 7.8147

Since the calculated value of = 4.1142 is less than the critical value of = 7.8147, Fail to Reject H0.

Conclusion:

There is no relationship between handedness and gender.