Question

Question 4 a) Set-up the steps you would take to conduct a simple hypothesis test of any kind. Explain in some detail what is to be done in each of the steps. b) The distribution of a random sample of 1,000 UNAM students according to the sport they like most and country of origin is as follows: Country of Origin 20 Namibia Other SADC Country Rest of Africa Elsewhere Total Football 410 220 57 Sport Liked Most Basketball Others None 52 58 12 15 10 15 140 10 18 Total 500 300 100 100 1000 13 18 54 700 60 100 Is liking of sports associated with the country of origin of the studen? Perform a Chi-square test at 95% level of confidence and state what you conclude from the evidence of the sample.

Answer 1

a ) here we will use the chi-square test ins which step 1: we will introduce the null and alternative hypothesis

in step 2: we will define the rejection region

in step 3: we will find the computed value of tests statistic

in step 4: we will tell while we accept or reject the null hypothesis

in step 5 : we will find the conclusion

b ) let us consider H0: liking of sport associated with the country of origin

H1: liking of sport not associated with the country of origin

using excel we have

sport like most
Observed Frequencies
	Column variable						Calculations
country of Origin	Football	Basketball	Other	None	Total		fo-fe
Namibia	410	52	20	18	500		60	-18	-10	-32
Other SADC country	220	58	12	10	300		10	16	-6	-20
Rest of America	57	15	10	18	100		-13	1	4	8
Elsewhere	13	15	18	54	100		-57	1	12	44
Total	700	140	60	100	1000
Expected Frequencies
	Column variable
country of Origin	Football	Basketball	Other	None	Total		(fo-fe)^2/fe
Namibia	350	70	30	50	500		10.28571	4.628571	3.333333	20.48
Other SADC country	210	42	18	30	300		0.47619	6.095238	2	13.33333
Rest of America	70	14	6	10	100		2.414286	0.071429	2.666667	6.4
Elsewhere	70	14	6	10	100		46.41429	0.071429	24	193.6
Total	700	140	60	100	1000
Data
Level of Significance	0.05
Number of Rows	4
Number of Columns	4
Degrees of Freedom	9
Results
Critical Value	16.91898
Chi-Square Test Statistic	336.2705
p-Value	5.16E-67
Reject the null hypothesis

since the calculated value of the chi-square test is greater than critical value so we reject H0 and conclude that the liking of sport is not associated with the country of origin.