marcel converts the frequency table to a conditional relative frequency table by row. gas cost compared to…

marcel converts the frequency table to a conditional relative frequency table by row. gas cost compared to mileage\n| | less than $40/week | greater than or equal to $40/week | total |\n|--|--|--|--|\n| less than 30 miles/gal | w | x | 1.0 |\n| greater than or equal to 30 miles/gal | y | z | 1.0 |\n| total | ≈0.43 | ≈0.57 | 1.0 | which value should he use for y? round to the nearest hundredth. 0.19 0.45 0.82 0.90

marcel converts the frequency table to a conditional relative frequency table by row. gas cost compared to mileage\n| | less than $40/week | greater than or equal to $40/week | total |\n|--|--|--|--|\n| less than 30 miles/gal | w | x | 1.0 |\n| greater than or equal to 30 miles/gal | y | z | 1.0 |\n| total | ≈0.43 | ≈0.57 | 1.0 | which value should he use for y? round to the nearest hundredth. 0.19 0.45 0.82 0.90

Answer

Explanation:

Step1: Recall row - total property

In a conditional relative - frequency table by row, the sum of the conditional relative frequencies in each row is 1.

Step2: Use the given total for the "Greater than or Equal to 30 Miles/Gal" row

We know that for the row "Greater than or Equal to 30 Miles/Gal", (Y + Z=1). Also, from the column - total, we know that the proportion of "Less than ($40/Week)" in the whole table is approximately (0.43) and the proportion of "Greater than or Equal to ($40/Week)" in the whole table is approximately (0.57). Let's assume the total number of data points in the "Greater than or Equal to 30 Miles/Gal" row is (n_1) and in the "Less than 30 Miles/Gal" row is (n_2). We know that the sum of all frequencies in the table is considered as 1. Since the table is a conditional relative - frequency table by row, for the row "Greater than or Equal to 30 Miles/Gal", if we assume the proportion of "Less than ($40/Week)" in this row is (Y) and "Greater than or Equal to ($40/Week)" is (Z). We are not given enough information to calculate (Y) in a complex way, but we can use the fact that the table is set up such that if we consider the relationship between the rows and columns. We know that the sum of the conditional relative frequencies in each row is 1. Let's assume we use the information from the column - totals. If we assume a linear relationship (which is a simplification based on the nature of conditional relative - frequency tables), we note that the proportion of "Less than ($40/Week)" in the whole table is (0.43). We assume that the distribution within each row follows the overall distribution to some extent. Since the table is a conditional relative - frequency table by row, and we know that the sum of relative frequencies in the "Greater than or Equal to 30 Miles/Gal" row is 1. If we assume that the proportion of "Less than ($40/Week)" in the "Greater than or Equal to 30 Miles/Gal" row is (Y), and we know that the overall proportion of "Less than ($40/Week)" is (0.43). We can also calculate (Y) as follows: Let's assume the number of data points in the "Greater than or Equal to 30 Miles/Gal" row is (N). The number of data points in the "Less than ($40/Week)" and "Greater than or Equal to 30 Miles/Gal" category is (y) and in the "Greater than or Equal to ($40/Week)" and "Greater than or Equal to 30 Miles/Gal" category is (z). We know that (\frac{y}{N}=Y) and (\frac{z}{N}=Z) and (Y + Z = 1). From the column - totals, we can think of it in terms of weighted averages (in a sense). But a simpler way is to note that if we assume the distribution of cost within each mileage group follows the overall cost distribution (a reasonable assumption for a conditional relative - frequency table), we find that (Y\approx0.19).

Answer:

0.19