a researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and…

a researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. the sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. if these data were used for a chi - square test for independence, what is the expected frequency for registered females?\n\n12\n\n28\n\n40\n\n42

a researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. the sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. if these data were used for a chi - square test for independence, what is the expected frequency for registered females?\n\n12\n\n28\n\n40\n\n42

Answer

Explanation:

Step1: Calculate row - total of registered voters

The total number of registered voters is (30 + 40=70).

Step2: Calculate column - total of females

The total number of females is 40.

Step3: Calculate grand - total

The grand - total number of people in the sample is 100.

Step4: Use the formula for expected frequency in a chi - square test for independence

The formula for the expected frequency (E_{ij}=\frac{R_i\times C_j}{N}), where (R_i) is the row - total, (C_j) is the column - total and (N) is the grand - total. For registered females, (R = 70) (row - total of registered voters), (C = 40) (column - total of females) and (N = 100). So (E=\frac{70\times40}{100}=28).

Answer:

28