Question

A researcher wants to determine if the number of minutes spent watching television per day is independent of gender. A random sample of 315 adults was selected and the results are shown below. Is there enough evidence to conclude that the number of minutes spent watching television per day is related to gender? Test at the alpha=0.05 level of significance. Please show all work/calculations.

Minutes spent watching tv per day in table below:

GENDER	0-30	30-60	60-90	90-OVER
Male	25	35	75	45
Female	40	45	45	15

A) State and check the conditions that must be met in order to perform this test. If needed, include a sketch of any appropriate graphs.

B) State the hypothesis. Clearly label the population parameter(s).

C) Perform the test and state the test used, the P-value, and the decision. Round the P-value to 4 decimal places and Please show all work/calculations.

D) Write a conclusion using a complete sentence.

Answer 1

Ans:

a)Both variables are categorical variables,so we can sue chi square distribution.

b)

H₀:The number of minutes spent watching television per day is independent of gender.

Ha: The number of minutes spent watching television per day is not independent of gender.

c)Chi square test for independence:

	Observed(fo)
GENDER	0-30	30-60	60-90	90-OVER	Total
Male	25	35	75	45	180
Female	40	45	45	15	145
Total	65	80	120	60	325
	Expected(fe)
GENDER	0-30	30-60	60-90	90-OVER	Total
Male	36.00	44.31	66.46	33.23	180
Female	29.00	35.69	53.54	26.77	145
Total	65	80	120	60	325
	Chi square=(fo-fe)^2/fe
GENDER	0-30	30-60	60-90	90-OVER	Total
Male	3.361	1.955	1.097	4.168	10.582
Female	4.172	2.427	1.362	5.174	13.136
Total	7.534	4.382	2.459	9.343	23.717

Test statistic:

Chi square=23.717

df=(2-1)*(4-1)=3

p-value=CHIDIST(23.717,3)=0.0000

d)As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that the number of minutes spent watching television per day is not independent of gender.