Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another.Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range.The following contingency table presents these results. The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is ______.
A) 24.0
B) 26.0
C) 32.5
D) 52.0

Question

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another.Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range.The following contingency table presents these results.  The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is ______.
A) 24.0 
B) 26.0 
C) 32.5 
D) 52.0

Quizplus · Accepted Answer

To calculate the expected values for each cell, we need to first calculate the row and column totals, as well as the total sample size:
- Row 1 total (income < $50,000) = 140
- Row 2 total (income $50,000-$100,000) = 120
- Row 3 total (income > $100,000) = 140
- Column 1 total (credit score 350-550) = 100
- Column 2 total (credit score 550-650) = 100
- Column 3 total (credit score 650-750) = 100
- Column 4 total (credit score 750-850) = 100
- Grand total = 400

To calculate the expected value for a given cell, we use the formula:
(expected count) = (row total) * (column total) / (grand total)

For the cell in question (income < $50,000 and credit score 650-750), the expected count is:
(expected count) = (140) * (100) / (400) = 35 * 1/4 = 8.75

However, we cannot have a fraction of a person, so we need to round to the nearest whole number. Since 8.75 is closer to 9 than to 8, we round up to get an expected count of 9.

Therefore, the expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is 26.0, as there are 26 such individuals in our sample.

Suppose Bank of America Would Like to Investigate If the Credit