2) a public opinion survey explored the relationship between age and support for increasing the minimum…

2) 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.\n\n| | yes | no | no opinion | total |\n|--|--|--|--|--| \n| 18 to 30 | 25 | 20 | 5 | 50 |\n| 31 to 60 | 20 | 35 | 20 | 75 |\n| over 60 | 55 | 15 | 5 | 75 |\n| total | 100 | 70 | 30 | 200 |\n\na) give an example of a joint relative frequency and interpret it in context.\n\nb) give an example of a marginal relative frequency and interpret it in context.\n\nc) give an example of a conditional relative frequency and interpret it in context.

2) 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.\n\n| | yes | no | no opinion | total |\n|--|--|--|--|--| \n| 18 to 30 | 25 | 20 | 5 | 50 |\n| 31 to 60 | 20 | 35 | 20 | 75 |\n| over 60 | 55 | 15 | 5 | 75 |\n| total | 100 | 70 | 30 | 200 |\n\na) give an example of a joint relative frequency and interpret it in context.\n\nb) give an example of a marginal relative frequency and interpret it in context.\n\nc) give an example of a conditional relative frequency and interpret it in context.

Answer

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.