Question

1. a public opinion survey explored the relationship between age and support for increasing the minimum wage. the results are summarized in the two - way table below.

	yes	no	no opinion	total
31 to 60	20	35	20	75
over 60	55	15	5	75
total	100	70	30	200

a) give an example of a joint relative frequency and interpret it in context.

b) give an example of a marginal relative frequency and interpret it in context.

c) give an example of a conditional relative frequency and interpret it in context.

Explanation:

Step1: Define joint relative frequency

Joint relative frequency is the ratio of a cell - value to the total number of observations. For example, consider the number of 18 - to - 30 - year - olds who support the minimum wage increase. The joint relative frequency is $\frac{25}{200}=0.125$. This means that 12.5% of all the people surveyed are 18 - to - 30 - year - olds who support increasing the minimum wage.

Step2: Define marginal relative frequency

Marginal relative frequency is the ratio of a row - total or column - total to the grand total. For example, the marginal relative frequency of people who support the minimum wage increase is $\frac{100}{200}=0.5$. This means that 50% of all the people surveyed support increasing the minimum wage.

Step3: Define conditional relative frequency

Conditional relative frequency is the ratio of a cell - value to a row - total or column - total (depending on the condition). For example, among those over 60, the conditional relative frequency of those who support the minimum wage increase is $\frac{55}{75}\approx0.733$. This means that about 73.3% of people over 60 support increasing the minimum wage.

Answer:

a) Joint relative frequency: $\frac{25}{200}=0.125$. Interpretation: 12.5% of all surveyed are 18 - to - 30 - year - olds who support increasing the minimum wage.
b) Marginal relative frequency: $\frac{100}{200}=0.5$. Interpretation: 50% of all surveyed support increasing the minimum wage.
c) Conditional relative frequency: $\frac{55}{75}\approx0.733$. Interpretation: About 73.3% of people over 60 support increasing the minimum wage.