in exercises 1 and 2, use the two - way table to make another two - way table that shows the joint and…

in exercises 1 and 2, use the two - way table to make another two - way table that shows the joint and marginal relative frequencies.\n1.\n| |surfing style| | |\n|----|----|----|----|\n| |regular|advanced|total|\n|gender|male|86|24|110|\n| |female|77|18|95|\n|total|163|42|205|\n2.\n| |fishing license| | |\n|----|----|----|----|\n| |yes|no|total|\n|hunting license|yes|65|37|102|\n| |no|177|341|518|\n|total|242|378|620|
Answer
Explanation:
Step1: Calculate joint relative frequencies
Joint relative frequency = $\frac{\text{Cell - value}}{\text{Grand - total}}$. For example, for male and regular surfing style in the first table, the joint relative frequency is $\frac{86}{205}$. Calculate all cell - values in this way.
Step2: Calculate row - marginal relative frequencies
Row - marginal relative frequency = $\frac{\text{Row - total}}{\text{Grand - total}}$. For the male row in the first table, the row - marginal relative frequency is $\frac{110}{205}$. Calculate for all rows.
Step3: Calculate column - marginal relative frequencies
Column - marginal relative frequency = $\frac{\text{Column - total}}{\text{Grand - total}}$. For the regular surfing style column in the first table, the column - marginal relative frequency is $\frac{163}{205}$. Calculate for all columns.
First table (Surfing Style):
| Regular | Advanced | Total | |
|---|---|---|---|
| Male | $\frac{86}{205}\approx0.42$ | $\frac{24}{205}\approx0.12$ | $\frac{110}{205}\approx0.54$ |
| Female | $\frac{77}{205}\approx0.37$ | $\frac{18}{205}\approx0.09$ | $\frac{95}{205}\approx0.46$ |
| Total | $\frac{163}{205}\approx0.80$ | $\frac{42}{205}\approx0.20$ | $1$ |
Second table (Fishing and Hunting Licenses):
| Yes | No | Total | |
|---|---|---|---|
| Yes | $\frac{65}{620}\approx0.105$ | $\frac{37}{620}\approx0.06$ | $\frac{102}{620}\approx0.165$ |
| No | $\frac{177}{620}\approx0.285$ | $\frac{341}{620}\approx0.55$ | $\frac{518}{620}\approx0.835$ |
| Total | $\frac{242}{620}\approx0.39$ | $\frac{378}{620}\approx0.61$ | $1$ |