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

1= the test statistics is : ( )

2= The correct decision would be

		We will not reject the null and conclude that mean number of hours spent watching TV and gender are dependent
		We will not reject the null and conclude that mean number of hours spent watching TV and gender are independent
		We will reject the null and conclude that mean number of hours spent watching TV and gender are dependent
		We will reject the null and conclude that mean number of hours spent watching TV and gender are independent

3=  The critical value is

Answers only !!

Answer 1

(1) Here expected value for any given cell of contigency table = Total value in column * Total value in row/Total population

Expected value table

	Gender
Hours	Male	Female	total
Under 8	100	100	200
8 to 15	80	80	160
15 or more	70	70	140
Total	250	250	500

Chi-square table

	Gender
Hours	Male	Female	total
Under 8	1	1	2
8 to 15	0.3125	0.3125	0.625
15 or more	0.357143	0.357143	0.714286
Total	1.669643	1.669643	3.339286

Chi-square value = = 3.339

(2) Here dF = (r-1) * (c-1) = (3-1) * (2-1) = 2

Critical value = CHIINV(0.05,2) = 5.99

as Test statistic value is less than critical value so we would fail to reject the null hypothesis. We will not reject the null and conclude that mean number of hours spent watching TV and gender are independent. Option B is correct here.

(3) Critical value = 5.99