Question

A sample of film watchers were asked their age and whether they would recommend the film to others. The results are in the table below. UNDER 30 30 - 50 OVER 50 YES 55 56 29 NO 15 24 21 At the 0.05 level of significance, determine if age and opinion are dependent. Answer each of the following parts to build your hypothesis test. a. Identify Ho and H1 (1 point). b. Calculate all SIX expected frequencies (2 points). c. Calculate the test statistic (5 points). d. Determine the critical value (1 point). e. State whether you accept Ho or reject Ho (1 point).

Answer 1

a)Ho: age and opinion are independent,

Ha:  age and opinion are dependent,

b) as expected frequency =row total*column total/grand total

therefore below is table of expected frequency:

Ei=?row*?column/?total	<30	30-50	>50
yes	49.000	56.000	35.000
No	21.000	24.000	15.000

c)

applyinf chi square test:

chi square	=(Oi-Ei)2/Ei	<30	30-50	>50	Total
	yes	0.73	0.00	1.03	1.76
	No	1.71	0.000	2.400	4.11
	Total	2.45	0.00	3.43	5.878

  test statistic =5.878

d)

degree of freedom =(row-1)*(column-1)=(2-1)*(3-1)=2

for 2 df and 0.05 level critical value =5.991

e)as test statsitic is not greater than critical value we can not reject null hypothesis