Chapter 10.6, Problem 39HP

To determine

To discuss the conditional frequency are better than simple relative frequencies.

Explanation of Solution

Given information:

Discuss the conditional frequency are better than simple relative frequencies.

The relative frequency describes the proportion of the subjects jointly classified by a category of X and a category of Y where X and Y are two variables. The cells of the contingency table divided by the total provides the relative frequency. The sum of the relative frequency is 1.

The conditional frequency describe the frequency of one variable given the levels of the other variable. The cells of the contingency table divided by the row or column totals provide the conditional frequency. The sum of a conditional frequency is 1.

When both variables are random, you can describe the data using the relative frequency, the conditional frequency of Y given X, or the conditional distribution of X given Y.

When one variable is and explanatory variable (X, fixed) and the other a response variable (Y, random), the notion of a relative frequency is meaningless, and you should describe the data using the conditional frequency of Y given X.

consider two way frequency table of t-shirt sold:

  

Calculation:

1)Find number of females

  

2)Find out each conditional frequencies

Calculation:

The percentage female, give the preference for red:

Total red T-shirt sold=15,

Red T-shirt sold to females=10

Then, the percentage female, give the preference for red

  

Calculation:

The percentage female, give the preference for blue:

Total red t-shirt sold=25

Total blue t-shir sold to females=15

Then, the percentage female, give the preference for blue

  

Calculation:

The percentage female, give the preference for green:

Total red t-shirt sold=10

total green t-shir sold to females=5

Then, the percentage female, give the preference for green

  

Interpretation:

3)Interpret the result by comparing each conditional frequency to the percentage of all t-shirt sold to females.

-The percentage of females who prefer red is 67% that's greater than total female of 60%.

Hence, Gender appears to influence shirt color.

-The percentage of females who prefer blue is 60% that's same as total female of 60%.

Hence, Gender doesn't appears to influence shirt color.

-The percentage of females who prefer green is 50% that's less than total female of 60%.

Hence, Gender appears to influence shirt color.

When the conditional frequencies for the row are the same or similar the variables are not associated with each other.