Question

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1. A poll asked 15 men in two age groups, 30 and younger and older than 30, whether they had facial hair (mustache, beard, sideburns, etc.). The results are recorded in the table.
Person Age group Facial hair
1 30 and younger Yes
2 30 and younger No
3 Older than 30 No
4 30 and younger No
5 Older than 30 No
6 Older than 30 Yes
7 Older than 30 Yes
8 Older than 30 No
9 30 and younger Yes
10 30 and younger Yes
11 Older than 30 Yes
12 30 and younger Yes
13 Older than 30 Yes
14 30 and younger No
15 Older than 30 Yes
(a) Create a two-way table of the data. Of the men surveyed, how many were 30 and older? How many men did not have facial hair?
a. Please include labels and totals.
(b) Create a two-way relative frequency table that displays the relative frequency of the men 30 and younger and of the men older than 30 who had or did not have facial hair. Express your answers as decimals written to three decimal places.
(c) What is the percentage of men older than 30 who had facial hair?
Answer:
Two way table:
Relative frequency table:
(both tables had 4 slots vertically and 4 slots horizontally)

Answer 1

Answer: ------ Facial hair ------

Age

Yes No Total

30 and younger 0.267 0.200 0.467

older than 30 0.333 0.200 0.533

Total 0.600 0.400 1.000

Explanation:

1. Count the number of people for each category:

a) People who were 30 and younger and had facial hair:

1: 30 and younger. Yes

9: 30 and younger. Yes

10: 30 and younger. Yes

12: 30 and younger. Yes

Total: 4 people were 30 and younger and had facial hair

b) People who were 30 and younger and did not have facial hair:

2: 30 and younger.No

4: 30 and younger. No

14: 30 and younger. No

Total: 3 people were 30 and younger and did not have facial hair

c) People who were older than 30 and had facial hair:

6: Older than 30. Yes

7: Older than 30.Yes

11: Older than 30. Yes

13: Older than 30. Yes

15: Older than 30. Yes

Total: 5 people were older than 30 and had facial hair.

d) People who were older than 30 and did not have facial hair:

3: Older than 30. No

5: Older than 30. No

8: Older than 30. No

Total: 3 people were older than 30 and did not have facial hair.

2. Build a two way table with the absolute frequencies:

------ Facial hair ------

Yes No Total

Age

30 and younger 4 3 7

older than 30 5 3 8

Total 9 6 15

3. To build the two-way relative frequency table, divive each absolute frequency by the total number of men (15):

These are the quotients:

4/15 = 0.267

3/15 = 0.200

7/15 = 0.467

5/15 = 0.333

3/15 = 0.200

8/15 = 0.533

9/15 = 0.600

6/15 = 0.400

15/15 = 1.000

Now write the table with the relative frequencies:

-------- Facial hair --------

Yes No Total

Age

30 and younger 0.267 0.200 0.467

older than 30 0.333 0.200 0.533

Total 0.600 0.400 1.000

And that is the requested table written to three decimal places.