Questions: Observed Group 1 Group 2 Total Success 15 12 27 Failure 27 28 55 Total 42 40 82 Compute the expected count for Group 1 Success. Use a calculator or R. Round to one decimal place. Remember that the formula for expected counts is: Expected Count = (Row Total)(Column Total)/(Table Total) Answer:

Observed Group 1 Group 2 Total Success 15 12 27 Failure 27 28 55 Total 42 40 82 Compute the expected count for Group 1 Success. Use a calculator or R. Round to one decimal place. Remember that the formula for expected counts is: Expected Count = (Row Total)(Column Total)/(Table Total) Answer:
Transcript text: Observed Group 1 Group 2 Total \begin{tabular}{llll} Success 15 & 12 & 27 \\ Failure & 27 & 28 & 55 \\ Total $\quad 42$ & 40 & 82 \end{tabular} Compute the expected count for Group 1 Success. Use a calculator or R. Round to one decimal place. Remember that the formula for expected counts is: \[ \text { Expected Count }=\frac{(\text { Row Total })(\text { Column Total })}{\text { Table Total }} \] Answer: $\square$
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Solution

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Solution Steps

To compute the expected count for Group 1 Success, we use the formula for expected counts in a contingency table. The expected count is calculated by multiplying the total of the row containing the cell of interest by the total of the column containing the cell of interest, and then dividing by the overall total of the table. In this case, the row total for Success is 27, the column total for Group 1 is 42, and the table total is 82.

Step 1: Identify the Values

We are given the following values from the contingency table:

  • Row total for Success: \( 27 \)
  • Column total for Group 1: \( 42 \)
  • Table total: \( 82 \)
Step 2: Apply the Expected Count Formula

The expected count for Group 1 Success can be calculated using the formula: \[ \text{Expected Count} = \frac{(\text{Row Total})(\text{Column Total})}{\text{Table Total}} \] Substituting the known values: \[ \text{Expected Count} = \frac{(27)(42)}{82} \]

Step 3: Perform the Calculation

Calculating the expected count: \[ \text{Expected Count} = \frac{1134}{82} \approx 13.8 \]

Final Answer

The expected count for Group 1 Success is \\(\boxed{13.8}\\).

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