Question

1. a survey was taken of 100 families with one child and 86 families with two or more children to determine whether they were saving for college. of those, 94 of the families with one child and 60 of the families with two or more children were saving for college. organize these results in a two - way table. then find and interpret the marginal frequencies.

Explanation:

Step1: Define Categories

We have two categories: number of children (one child, two or more children) and saving for college (yes, no).

Step2: Calculate "No" for Each Group

• For one - child families: Total = 100, Saving = 94, so Not Saving = \(100 - 94=6\)
• For two - or - more - children families: Total = 86, Saving = 60, so Not Saving = \(86 - 60 = 26\)

Step3: Create Two - Way Table

	Saving for College	Not Saving for College	Total
Two or More	60	26	86
Total	\(94 + 60=154\)	\(6+26 = 32\)	\(100 + 86=186\)

Step4: Find Marginal Frequencies

• Marginal frequency for "One Child" total: 100 (total number of one - child families). This means out of all surveyed families, 100 have one child.
• Marginal frequency for "Two or More" total: 86 (total number of families with two or more children). This means out of all surveyed families, 86 have two or more children.
• Marginal frequency for "Saving for College" total: 154 (total number of families saving for college). This means out of all 186 surveyed families, 154 are saving for college.
• Marginal frequency for "Not Saving for College" total: 32 (total number of families not saving for college). This means out of all 186 surveyed families, 32 are not saving for college.
• The grand total (marginal frequency for all families) is \(100 + 86=186\), which is the total number of families surveyed.

Answer:

Two - Way Table:

	Saving for College	Not Saving for College	Total
Two or More	60	26	86
Total	154	32	186

Marginal Frequencies Interpretation:

• Total one - child families: 100 (100 families have one child).
• Total two - or - more - children families: 86 (86 families have two or more children).
• Total saving for college: 154 (154 families are saving for college).
• Total not saving for college: 32 (32 families are not saving for college).
• Grand total: 186 (186 families were surveyed).