1
TUT 3 on Ch 12 MEMORANDUM
Question 1
In order to determine what the opinions of sport enthusiasts of different genders’ were about
team SA’s performance at the Olympic Games before the start of the Games, a random
sample of 200 sport enthusiasts were asked how many gold medals the team will bring back.
The results are given in the following table with some of the expected frequencies, calculated
under the assumption that gender and opinion are independent, in brackets.
Number of medals Total
1 2 More than 2 medals
Gender Male 40 (35) 40 (35) 20 (𝑒 30 100
Female 30 (35) 30 (35) 40 (𝑒 30 100
Total 70 70 60 200
Complete the contingency table to test, at a 5% level, if there is an association between
gender and the opinion of sport enthusiasts. Use the critical value as well as the p-value
approach.
𝑒 𝑒 30
𝐻 : There is no association between gender and the opinion of sport enthusiasts.
(or Gender and opinion of sports enthusiasts are independent)
𝐻 : There is an association between gender and the opinion of sport enthusiasts.
(or Gender and opinion of sports enthusiasts are not independent or dependent)
Test Statistic:
𝑓 𝑒 40 35 40 30
𝜒 ⋯ 9.5238
𝑒 35 30
Rejection rule:
Critical value approach: On a 5% level of significance and 2 1 3 1 2 𝑑𝑓, the null
hypothesis will be rejected if the Test Statistic is bigger than 5.9915
Decision:
Reject 𝐻
5.9915.9
Conclusion: At 5% significance level there is enough evidence to conclude that there is an
association between gender and the opinion of sport enthusiasts
p-value approach:
0.005 𝑝 𝑣𝑎𝑙𝑢𝑒 0.01 and since values in this range is <0.05, same conclusion as above
TUT 3 on Ch 12 MEMORANDUM
Question 1
In order to determine what the opinions of sport enthusiasts of different genders’ were about
team SA’s performance at the Olympic Games before the start of the Games, a random
sample of 200 sport enthusiasts were asked how many gold medals the team will bring back.
The results are given in the following table with some of the expected frequencies, calculated
under the assumption that gender and opinion are independent, in brackets.
Number of medals Total
1 2 More than 2 medals
Gender Male 40 (35) 40 (35) 20 (𝑒 30 100
Female 30 (35) 30 (35) 40 (𝑒 30 100
Total 70 70 60 200
Complete the contingency table to test, at a 5% level, if there is an association between
gender and the opinion of sport enthusiasts. Use the critical value as well as the p-value
approach.
𝑒 𝑒 30
𝐻 : There is no association between gender and the opinion of sport enthusiasts.
(or Gender and opinion of sports enthusiasts are independent)
𝐻 : There is an association between gender and the opinion of sport enthusiasts.
(or Gender and opinion of sports enthusiasts are not independent or dependent)
Test Statistic:
𝑓 𝑒 40 35 40 30
𝜒 ⋯ 9.5238
𝑒 35 30
Rejection rule:
Critical value approach: On a 5% level of significance and 2 1 3 1 2 𝑑𝑓, the null
hypothesis will be rejected if the Test Statistic is bigger than 5.9915
Decision:
Reject 𝐻
5.9915.9
Conclusion: At 5% significance level there is enough evidence to conclude that there is an
association between gender and the opinion of sport enthusiasts
p-value approach:
0.005 𝑝 𝑣𝑎𝑙𝑢𝑒 0.01 and since values in this range is <0.05, same conclusion as above
