Answer:
(a) See the table below
- How many men were 30 and younger than 30: 6
- How many men did not have facial hair: 5
(b) See the table below
(c) What percentage of men older than 30 had facial hair? 50%
Explanation:
(a) Create a two-way table of the data
Count the number of men in each group
- 1, 9, 10, and 12: 30 and younger, Yes.
- 2, and 4: 30 and younger, No
- 6, 7, and 11: Older than 30, Yes
- 3, 5, and 8: Older than 30, No
Put the information in the two-way table:
Has Facial Hair No Facial Hair Total
Older than 30 3 3 6
30 and younger 4 2 6
Total 7 5 12
i) Of the men surveyed how many were 30 and younger?
- Read the total of the second row: 6
ii) Of the men surveyed how many men did not have facial hair:
- Read the total of the second column: 5
(b) Create a two way relative frequency table that displays the relative frequencies
Determine each relative frequency divide each cell by the total number of men of the sample, 12:
- First row with first column: 3/12 = 0.250
- First row with second column: 3/12 = 0.250
- First row with third column: 6/12 = 0.500
- Second row with first column: 4/12 = 0.333
- Second row with second colum: 2/12 = 0.167
- Second row with third column: 6/12 = 0.500
- Third row with first column: 7/12 = 0.583
- Third row with second column: 5/12 = 0.417
- Third row with third column: 12/12 = 1.000
Put the relative frequencies in the table:
Has Facial Hair No Facial Hair Total
Older than 30 0.250 0.250 0.500
30 and younger 0.333 0.167 0.500
Total 0.583 0.417 1.000
(c) What percentage of men older than 30 had facial hair?
This is a conditional probability. You must divide the relative frequency in the intersection of the men older than 30 and has facial hair, which is 0.250 by the relative frequency of total men older than 30, which is 0.500.
Thus, this is 0.250/0.500 = 0.500.
Now, convert to percent: 0.500 = 50.0%
