Question

In a study of Americans from a variety of professions were asked if they considered themselves left-handed, right-handed, or ambidextrous. The results are given below:

Profession	right	left	ambidextrous	total
Teacher	101	10	7	118
Engineer	115	26	7	148
Surgeon	121	5	6	132
Firefighter	83	16	6	105
Police Officer	116	10	6	132
Total	536	67	32	635

Is there enough evidence to conclude that proportion of left-handed surgeons is less than the proportion of left-handed Engineers? Make sure you show all the steps of the test.

Answer 1

Surgeon --1

Engineer--2

We have

n1= 132 , x1 = 5

n2= 148 , x2= 26

p1= 5/132 = 0.03788

p2 = 26/148 = 0.1757

pooled

  

Standard Error (p1-p2) =

H0: P1=P2 That is the proportion of left-handed surgeons and the proportion of left-handed Engineers is same.

H1: P1< P2 That is the proportion of left-handed surgeons is less than the proportion of left-handed Engineers.

(one tailed test)

Let = 0.05 level of significance

Test statistic

p value = 0.00015

Decision : p value (0.00015) < 0.05

   or

   test statistics (-3.6183) < -1.645 (critical value of Z at 5% for one tail )

Reject H0

Conclusion:

We conclude that

There is enough evidence to conclude that proportion of left-handed surgeons is less than the proportion of left-handed Engineers .