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TUT 3 on Ch 12 Preparation
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 (𝑒𝑒13 ) 100
Female 30 (35) 30 (35) 40 (𝑒𝑒23 ) 100
Total 70 70 60 200
Complete the contingency table to test, at a 5% level of significance, if there is an
association between gender and the opinion of sport enthusiasts. Use the critical value as
well as the p-value approach.
Questions 2 to 6 are based on the following information:
ABC Bank wants to investigate whether there is a difference in the rating given by males
and females on their perception of the service that ABC Bank provides.
Service rating
Gender Excellent Average Poor Total
Male 116 94 90 300
Female 134 100 116 350
Total 250 194 206 650
A Chi squared test is done to test whether gender and service rating are independent.
Given: χ 2 test statistic = 0.9224
Question 2
Under the null hypothesis of independence, the probability that a randomly selected
respondent will be female and that she will give an excellent service rating is:
Question 3
Show how your answer in question 2 relates to the fomula:
Expected number of females that give an excellent service rating is
= (row total of 350) x (collumn total of 250) / grand total of 650
Question 4
With the critical value approach the decision rule is: Reject H 0 at a 5% level of
significance if:
Question 5
The decision that can be made is:
Question 6
The conclusion that can be drawn at a 5% level of significance, is:
TUT 3 on Ch 12 Preparation
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 (𝑒𝑒13 ) 100
Female 30 (35) 30 (35) 40 (𝑒𝑒23 ) 100
Total 70 70 60 200
Complete the contingency table to test, at a 5% level of significance, if there is an
association between gender and the opinion of sport enthusiasts. Use the critical value as
well as the p-value approach.
Questions 2 to 6 are based on the following information:
ABC Bank wants to investigate whether there is a difference in the rating given by males
and females on their perception of the service that ABC Bank provides.
Service rating
Gender Excellent Average Poor Total
Male 116 94 90 300
Female 134 100 116 350
Total 250 194 206 650
A Chi squared test is done to test whether gender and service rating are independent.
Given: χ 2 test statistic = 0.9224
Question 2
Under the null hypothesis of independence, the probability that a randomly selected
respondent will be female and that she will give an excellent service rating is:
Question 3
Show how your answer in question 2 relates to the fomula:
Expected number of females that give an excellent service rating is
= (row total of 350) x (collumn total of 250) / grand total of 650
Question 4
With the critical value approach the decision rule is: Reject H 0 at a 5% level of
significance if:
Question 5
The decision that can be made is:
Question 6
The conclusion that can be drawn at a 5% level of significance, is:
