Question

A random sample of 500 male and female adults was asked the amount of time each person spent watching TV last week. Their responses are shown at the right. At the 0.05 significance level, does it appear that the amount of time spent watching TV is related to the gender of the viewer?

Hours/Gender	Male	Female	Total
Under 8	90	110	200
8 to 15	85	75	160
15 or more	75	65	140
Total	250	250	500

Which test would be used to properly analyze the data in this experiment?

		χ 2 test for difference among more than two proportions
		none of the above
		χ 2 test for difference between two proportions
		χ 2 test of independence

answer only !!

Answer 1

We want to test the amount of time spent watching TV is related to the gender of the viewer.

To Analyze the data in this experiment the chi-square( χ 2) test of independence is appropriate.

Hypothesis:

H_{​​​​​​0} : The amount of time spent watching TV is not related to the gender of the viewer.

Against

H_{​​​​​​0} : The amount of time spent watching TV is not related to the gender of the viewer.

Test statistic:

Where,

m= number of rows= 3

n=number of columns=2

N=grand total

E_{​​​​​​ij} =expected frequency of i^{​​​​​​th} row and j^{​​​​​th} column

Observation table:

O​​​​₁₂ =110

Hours\Gender	Male	Female	Row total
Under 8	O​​​​​11 =90	R1= 200
8 to 15	O​​​​​21 = 85	O​​​​​22 = 75	R2=160
15 or more	O31 =75	O32 = 65	R3=140
Column total	C1=250	C2= 250	N=500

Observation table:

O​​​​​​ij	E​​​​​​ij	O2​​​​​​ij​​​ / E ij
90	100	81
110	100	121
85	80	90.3125
75	80	70.3125
75	70	80.3571
65	70	60.3571
		=503.3392

The calculated test statistic is

Critical value at (m-1)(n-1)=(3-1)(2-1)=2*1=2 degrees of freedom at 5% level of Significance is:

Therefore we failed to reject the null hypothesis at 5% level of Significance.

Conclusion:

There insufficient evidence to conclude that the amount of time spent watching TV is related to the gender of the viewer.