Question

Gender and handedness (right-handed or left-handed) are recorded for a randomly-selected sample of adults. Of the 100 women in the sample, 92 women are right-handed. Of the 80 men in the sample, 70 men are right-handed.
a.   Write a two-way table of observed counts.
b.   Calculate the conditional distribution of handedness, given gender.
c.   Describe the conditional distribution above in a few sentences.
d.   Determine expected counts for all combinations of gender and handedness.
e.   Calculate the value of the chi-square test statistic.
f.   Now, show all the steps of the hypothesis test, making sure to write out the conclusion in non-technical language.

Answer 1

b)

given Male

P(right)=70/80

P(left)=10/80

given female

P(right)=92/100

P(left)=8/100

c)

in genral conditional probability for right- handedness is more than hat of left

d) , e) and f)

			c1	c2	total
		r1	70	10	80
		r2	92	8	100
		total	162	18	180
		Oi	70	10	92	8
		Ei	72	8	90	10
							TS
		(O--Ei)^2/Ei	0.055556	0.5	0.044444	0.4	1
		critical value	3.84
	p-value	0.317310508

TS = 1

TS < critical value

we fail to reject the null hypothesis

there is not enough evidence to conclude that Gender and handedness are dependent