# Statistics MCQs – Tests for Qualitative Data Part 4

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61. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident and the extent of his or her injuries, being either minor injuries, major injuries or death. The accident reports from 155 accidents are examined, 45 involving minor injuries to the cyclist, 62 involving major injuries and 48 involving the death of the cyclist. In each case the number of accidents in which a helmet was worn and in which a helmet was not worn is recorded. In 10 of the accidents involving minor injuries, a helmet was not worn. The number of cases of a cyclist not wearing a helmet where the accident involved major injuries is 42 and in the case of death, 31 times a helmet was not worn by the cyclist. What is the test statistic value of the appropriate test in this case?

a. 1.1

b. 4.9

c. 14.3

d. 7.36

e. 25.1

Answer: E

62. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. 35 males and 21 females are described as having short hair. What is the value of the test statistic in this case?

a. 14.5

b. 6.5

c. 7.8

d. 23.7

e. 2.7

Answer: A

63. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. 29 males and 21 females are described as having short hair. What is the value of the test statistic in this case?

a. 14.5

b. 6.5

c. 7.8

d. 23.7

e. 2.7

Answer: B

64. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. 35 males and 27 females are described as having short hair. What is the value of the test statistic in this case?

a. 14.5

b. 6.5

c. 7.8

d. 23.7

e. 2.7

Answer: C

65. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. 40 males and 21 females are described as having short hair. What is the value of the test statistic in this case?

a. 14.5

b. 6.5

c. 7.8

d. 23.7

e. 2.7

Answer: D

66. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. 35 males and 34 females are described as having short hair. What is the value of the test statistic in this case?

a. 14.5

b. 6.5

c. 7.8

d. 23.7

e. 2.7

Answer: E

67. A test of association is conducted using a contingency table, to test whether there is any relationship between gender and preference for a certain type of sport. 100 people are interviewed, 64 females and 36 males, and each is asked to choose their favourite sport from a list which consists of rugby, cricket, soccer and swimming. The test statistic value for the test is 8.26. If the test is conducted at the 5 % level of significance, which of the following conclusions would be correct?

a. the null hypothesis cannot be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

b. the null hypothesis cannot be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

c. the null hypothesis can be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

d. the null hypothesis can be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

e. the null hypothesis can be accepted and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

Answer: D

68. A test of association is conducted using a contingency table, to test whether there is any relationship between gender and preference for a certain type of sport. 100 people are interviewed, 64 females and 36 males, and each is asked to choose their favourite sport from a list which consists of rugby, cricket, soccer and swimming. The test statistic value for the test is 8.26. If the test is conducted at the 2.5 % level of significance, which of the following conclusions would be correct?

a. the null hypothesis cannot be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

b. the null hypothesis cannot be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

c. the null hypothesis can be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

d. the null hypothesis can be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

e. the null hypothesis can be accepted and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

Answer: A

69. A test of association is conducted using a contingency table, to test whether there is any relationship between gender and preference for a certain type of sport. 100 people are interviewed, 64 females and 36 males, and each is asked to choose their favourite sport from a list which consists of rugby, cricket, soccer, basketball and swimming. The test statistic value for the test is 8.26. If the test is conducted at the 5 % level of significance, which of the following conclusions would be correct?

a. the null hypothesis cannot be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

b. the null hypothesis cannot be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

c. the null hypothesis can be rejected and therefore we can conclude that there is no relationship between gender and preference for a certain type of sport

d. the null hypothesis can be rejected and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

e. the null hypothesis can be accepted and therefore we can conclude that there is a relationship between gender and preference for a certain type of sport

Answer: A

70. We wish to examine the relationship between gender and belief in love at first sight. 45 males and 60 females are asked whether they believe in love at first sight. The only possible answers to the question posed are “yes” or “no” . 20 males and 35 females answer yes. What is the most correct conclusion for the appropriate hypothesis test to be conducted in this case?

a. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are independent

b. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

c. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are independent

d. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

e. The p-value for this test is between 0.01 and 0.025 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

Answer: C

71. We wish to examine the relationship between gender and belief in love at first sight. 45 males and 60 females are asked whether they believe in love at first sight. The only possible answers to the question posed are “yes” or “no” . 15 males and 46 females answer yes. What is the most correct conclusion for the appropriate hypothesis test to be conducted in this case?

a. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are independent

b. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

c. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are independent

d. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

e. The p-value for this test is between 0.01 and 0.025 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

Answer: B

72. We wish to examine the relationship between gender and belief in love at first sight. 45 males and 60 females are asked whether they believe in love at first sight. The only possible answers to the question posed are “yes” or “no” . 20 males and 40 females answer yes. What is the most correct conclusion for the appropriate hypothesis test to be conducted in this case?

a. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are independent

b. The p-value for this test is less than 0.005 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

c. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are independent

d. The p-value for this test is more than 0.10 therefore we do not reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

e. The p-value for this test is between 0.01 and 0.025 therefore we reject the null hypothesis and conclude that gender and belief in love at first sight are dependent

Answer: E

73. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident or not, and the extent of his or her injuries, being either minor injuries, major injuries or death. The test statistic value is calculated as being 1.1. What is the approximate p-value for the test?

a. p-value > 0.1

b. 0.05 < p-value < 0.1

c. 0.025 < p-value < 0.05

d. 0.01 < p-value < 0.025

e. p-value < 0.005

Answer: A

74. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident or not, and the extent of his or her injuries, being either minor injuries, major injuries or death. The test statistic value is calculated as being 4.9. What is the approximate p-value for the test?

a. p-value > 0.1

b. 0.05 < p-value < 0.1

c. 0.025 < p-value < 0.05

d. 0.01 < p-value < 0.025

e. p-value < 0.005

Answer: B

75. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident or not, and the extent of his or her injuries, being either minor injuries, major injuries or death. The test statistic value is calculated as being 6.2. What is the approximate p-value for the test?

a. p-value > 0.1

b. 0.05 < p-value < 0.1

c. 0.025 < p-value < 0.05

d. 0.01 < p-value < 0.025

e. p-value < 0.005

Answer: C

76. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident or not, and the extent of his or her injuries, being either minor injuries, major injuries or death. The test statistic value is calculated as being 8.3. What is the approximate p-value for the test?

a. p-value > 0.1

b. 0.05 < p-value < 0.1

c. 0.025 < p-value < 0.05

d. 0.01 < p-value < 0.025

e. p-value < 0.005

Answer: D

77. A test of association using a contingency table is conducted in order to test whether there is a relationship between whether a cycling helmet is worn by a cyclist involved in an accident or not, and the extent of his or her injuries, being either minor injuries, major injuries or death. The test statistic value is calculated as being 11.7. What is the approximate p-value for the test?

a. p-value > 0.1

b. 0.05 < p-value < 0.1

c. 0.025 < p-value < 0.05

d. 0.01 < p-value < 0.025

e. p-value < 0.005

Answer: E

78. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. The calculated test statistic of the appropriate test is 2.69. What conclusion can be made at the 5 % level of significance?

a. we do not reject H_{0} and conclude that gender and length of hair are independent

b. we do not reject H_{0} and conclude that gender and length of hair are dependent

c. we reject H_{0} and conclude that gender and length of hair are independent

d. we reject H_{0} and conclude that gender and length of hair are dependent

e. not enough data information is available for us to make a decision in this case

Answer: A

79. We wish to examine whether there is a relationship between gender and length of hair. 50 males and 62 females are observed and each is noted as having either “long” or “short” hair, according to predetermined criteria. The calculated test statistic of the appropriate test is 6.87. What conclusion can be made at the 5 % level of significance?

a. we do not reject H_{0} and conclude that gender and length of hair are independent

b. we do not reject H_{0} and conclude that gender and length of hair are dependent

c. we reject H_{0} and conclude that gender and length of hair are independent

d. we reject H_{0} and conclude that gender and length of hair are dependent

e. not enough data information is available for us to make a decision in this case

Answer: D