Question

odeling with mathematics

1. a survey asks 60 teachers and 48 parents whether school uniforms reduce distractions in school. of those, 49 teachers and 18 parents say uniforms reduce distractions in school. draw and organize these results in a two - way table. then find and interpret the marginal frequencies. (see example 1)

two - way table with columns: role (teachers, parents, total) and rows: response (yes, no, total). yes row: teachers 49, parents 18; total row: teachers 60, parents 48
108 people were surveyed,
60 teachers were surveyed,
48 parents were surveyed
67 people said yes,
41 people said no.

Explanation:

Step1: Complete the two - way table (Yes - Total)

To find the total number of people who said "Yes", we add the number of teachers who said "Yes" and the number of parents who said "Yes". So, \(49 + 18=67\).

Step2: Complete the two - way table (Teachers - No)

The total number of teachers surveyed is 60, and 49 of them said "Yes". So the number of teachers who said "No" is \(60 - 49 = 11\).

Step3: Complete the two - way table (Parents - No)

The total number of parents surveyed is 48, and 18 of them said "Yes". So the number of parents who said "No" is \(48 - 18=30\).

Step4: Complete the two - way table (No - Total)

To find the total number of people who said "No", we add the number of teachers who said "No" and the number of parents who said "No". So, \(11+30 = 41\).

Step5: Complete the two - way table (Grand Total)

To find the grand total of people surveyed, we add the total number of teachers and the total number of parents. So, \(60 + 48=108\). Also, we can verify by adding the total number of people who said "Yes" and the total number of people who said "No": \(67+41 = 108\).

The completed two - way table is:

Response	Role
Yes	49	18	67
No	11	30	41
Total	60	48	108

Interpretation of Marginal Frequencies:

• The marginal frequency for the "Total" row (grand total) is 108, which means 108 people were surveyed in total.
• The marginal frequency for the "Teachers" column (total) is 60, which means 60 teachers were surveyed.
• The marginal frequency for the "Parents" column (total) is 48, which means 48 parents were surveyed.
• The marginal frequency for the "Yes" row (total) is 67, which means 67 people (49 teachers and 18 parents) said that school uniforms reduce distractions.
• The marginal frequency for the "No" row (total) is 41, which means 41 people (11 teachers and 30 parents) said that school uniforms do not reduce distractions.

Answer:

The completed two - way table is as above. The marginal frequencies are: 108 people were surveyed, 60 teachers were surveyed, 48 parents were surveyed, 67 people said yes, and 41 people said no. The interpretations are as given above.