Questions: Westminster Financial has released a summary of investor and investment package information from the past fiscal year. During this time, Westminster provided a choice among several pre-designed investment packages. The investment packages were classified according to two variables: riskiness of investment package chosen ("Risky", "Moderate/mixed", and "Conservative") and age of investor ("Under 35", "35-49", or " 50 +"). Suppose that we're interested in the possible relationship between the age of the investor and the riskiness of the investment package the investor chose. The following contingency table gives a summary of the information released by Westminster regarding age and riskiness of investment package for 150 investors. In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, riskiness of investment package chosen and age of investor, are independent. Round your answers to two or more decimal places.

Westminster Financial has released a summary of investor and investment package information from the past fiscal year. During this time, Westminster provided a choice among several pre-designed investment packages. The investment packages were classified according to two variables: riskiness of investment package chosen ("Risky", "Moderate/mixed", and "Conservative") and age of investor ("Under 35", "35-49", or " 50 +"). Suppose that we're interested in the possible relationship between the age of the investor and the riskiness of the investment package the investor chose. The following contingency table gives a summary of the information released by Westminster regarding age and riskiness of investment package for 150 investors. In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, riskiness of investment package chosen and age of investor, are independent. Round your answers to two or more decimal places.
Transcript text: Westminster Financial has released a summary of investor and investment package information from the past fiscal year. During this time, Westminster provided a choice among several pre-designed investment packages. The investment packages were classified according to two variables: riskiness of investment package chosen ("Risky", "Moderate/mixed", and "Conservative") and age of investor ("Under 35", "35-49", or " 50 +"). Suppose that we're interested in the possible relationship between the age of the investor and the riskiness of the investment package the investor chose. The following contingency table gives a summary of the information released by Westminster regarding age and riskiness of investment package for 150 investors. In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, riskiness of investment package chosen and age of investor, are independent. Round your answers to two or more decimal places.
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Solution

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Solution Steps

Step 1: Calculate Expected Frequencies

To calculate the expected frequencies in a contingency table under the assumption of independence, we use the formula:

$$E_{ij} = \frac{R_i \times C_j}{G}$$

where $E_{ij}$ is the expected frequency for the cell at the intersection of the $i$th row and $j$th column, $R_i$ is the total frequency for the $i$th row, $C_j$ is the total frequency for the $j$th column, and $G$ is the grand total of all frequencies in the table.

Step 2: Detailed Calculations

For cell (1, 1): $E_{1,1} = \frac{50}{150} \times 60 = 20$

For cell (1, 2): $E_{1,2} = \frac{50}{150} \times 54 = 18$

For cell (1, 3): $E_{1,3} = \frac{50}{150} \times 36 = 12$

For cell (2, 1): $E_{2,1} = \frac{45}{150} \times 60 = 18$

For cell (2, 2): $E_{2,2} = \frac{45}{150} \times 54 = 16.2$

For cell (2, 3): $E_{2,3} = \frac{45}{150} \times 36 = 10.8$

For cell (3, 1): $E_{3,1} = \frac{55}{150} \times 60 = 22$

For cell (3, 2): $E_{3,2} = \frac{55}{150} \times 54 = 19.8$

For cell (3, 3): $E_{3,3} = \frac{55}{150} \times 36 = 13.2$

Final Answer:

The expected frequencies for each cell in the contingency table, rounded to the specified number of decimal places, are as follows:

Cell (1, 1): 20 Cell (1, 2): 18 Cell (1, 3): 12 Cell (2, 1): 18 Cell (2, 2): 16.2 Cell (2, 3): 10.8 Cell (3, 1): 22 Cell (3, 2): 19.8

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