Mean: - 58.67 Median - 62.18 Class Interval Yes No Total 18 – 34 7 2 9 35 – 44 3
ID: 3177146 • Letter: M
Question
Mean: - 58.67
Median - 62.18
Class Interval
Yes
No
Total
18 – 34
7
2
9
35 – 44
3
2
5
45 – 54
5
5
10
55 and over
41
35
76
56
44
100
Answers needed for G an H ONLY
(g) Use the contingency table to find the probability that a randomly selected person from
the sample:
(i) is 18 – 34 years of age and answered Yes;
(ii) answered Yes, given that the person is 18 – 34 years;
(iii) is 18 – 34 years of age, given that the person answered Yes;
(iv) is 18 - 34 years of age or answered Yes.
(h) Test the claim that the mean age of the people who would say yes to the survey
question is 60 years or older. Use = 0.10 and assume that the population is normally
distributed.
Class Interval
Yes
No
Total
18 – 34
7
2
9
35 – 44
3
2
5
45 – 54
5
5
10
55 and over
41
35
76
56
44
100
Explanation / Answer
the probability that a randomly selected person from the sample:
(i) is 18 – 34 years of age and answered Yes;
Probability that a randomly selected person from the sample is 18 – 34 years of age and answered Yes =
Number of persons whose age is 18-34 and answered yes / Total number of persons
From the table, Number of persons whose age is 18-34 and answered yes = 7
Total number of persons = 100
Probability that a randomly selected person from the sample is 18 – 34 years of age and answered Yes = 7/100
Probability that a randomly selected person from the sample
(ii) answered Yes, given that the person is 18 – 34 years;
Probability that a randomly selected person from the sample answered Yes, given that the person is 18 – 34 years =
Number of persons answered yes under the group 18-34 / Total number of persons in the group 18-34
From the table, Number of persons answered yes in the group 18-34 = 7
Total number of persons under the group 18-34 = 9
Probability that a randomly selected person from the sample answered Yes, given that the person is 18 – 34 years =7/9
(iii) is 18 – 34 years of age, given that the person answered Yes;
Probability that a randomly selected person from the sample is 18 – 34 years of age, given that the person answered Yes
= Number of persons under the group 18-34 who answered yes / Total number of persons who answered Yes
From the table, Number of persons under the group 18-34 who answered yes = 7
Total number of persons who answered Yes = 56
Probability that a randomly selected person from the sample is 18 – 34 years of age, given that the person answered Yes = 7/56
(iv) is 18 - 34 years of age or answered Yes.
Probability that a randomly selected person from the sample is 18 - 34 years of age or answered Yes. =
Probability that a randomly selected person from the sample is 18-34 + Probability that a randomly selected person from the sample answered Yes - Probability that a randomly selected person from the sample is 18-34 and answered yes.
Probability that a randomly selected person from the sample is 18-34 = Number of persons whose age is 18-34 / Total number of persons
From the table
Number of persons whose age is 18-34 = 9
Total number of persons = 100
Probability that a randomly selected person from the sample is 18-34 = 9/100
Probability that a randomly selected person from the sample answered Yes = Number of persons whose answered yes / Total number of persons
Number of persons whose answered yes= 56
Total number of persons = 100
Probability that a randomly selected person from the sample who answered yes = 56/100
From (i)
Probability that a randomly selected person from the sample is 18 – 34 years of age and answered Yes = 7/100
Probability that a randomly selected person from the sample is 18 - 34 years of age or answered Yes. =
Probability that a randomly selected person from the sample is 18-34 + Probability that a randomly selected person from the sample answered Yes - Probability that a randomly selected person from the sample is 18-34 and answered yes.
= 9/100 + 56/100 - 7/100 = 58/100
Class Interval Yes No Total 18 – 34 7 2 9 35 – 44 3 2 5 45 – 54 5 5 10 55 and over 41 35 76 Total 56 44 100