Skip to Main Content
Español

Topic 7 Homework (Nonadaptive)
Question 12 of 16 (1 point)|Question Attempt: 1 of Unlimited

Dennis

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16

Question 12
The following contingency table gives a summary of the data from 2000 trials of a visual experiment. Each of the trials was classified according to two variables: color vision of the participant ("Colorblind" or "Not colorblind") and trial outcome ("Hit", "Miss", "False alarm", or "Correct rejection"). 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, color vision of participant and trial outcome, are independent.
Round your answers to two or more decimal places.

Send data to Excel
Trial outcome
Hit	Miss	False alarm	Correct rejection	Total
Color vision of participant	Colorblind	77

22
23

70

192
Not colorblind	630
269
271
638
1808
Total	707	291	294	708	2000

Check

Save For Later

Submit
© 2024 McGraw Hill LLC. All Rights Reserved.
Terms of Use
|
Privacy Center
|
Accessibility
Clears your work.
Undoes your last action.

In this question, we are asked to fill in the blanks of the contingency table with the expected frequencies if the two variables (color vision of the participant and trial outcome) are independent.

The key to solving this is to use the formula for the expected frequency in a contingency table, which is:

\[
\text{Expected Frequency} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}
\]

Here is a step-by-step guide:

### Step 1: Set up the contingency table
We are given the following table:

| Trial Outcome         | Hit | Miss | False Alarm | Correct Rejection | Total |
|-----------------------|-----|------|-------------|-------------------|-------|
| **Colorblind**         | 77  | 22   | 23          | ___               | 192   |
| **Not Colorblind**     | 630 | 269  | 271         | 638               | 1808  |
| **Total**              | 707 | 291  | 294         | 708               | 2000  |

We are missing the "Correct Rejection" value for colorblind participants, and the "Hit" and "Miss" values for not colorblind participants.

### Step 2: Apply the expected frequency formula
Let's fill in the blanks.

#### 1. For **"Colorblind - Correct Rejection"**:
\[
\text{Expected Frequency (Colorblind - Correct Rejection)} = \frac{(192 \times 708)}{2000} = \frac{135936}{2000} = 67.968
\]
Rounded to two decimal places, the expected frequency is **67.97**.

#### 2. For **"Not Colorblind - Hit"**:
\[
\text{Expected Frequency (Not Colorblind - Hit)} = \frac{(1808 \times 707)}{2000} = \frac{1278256}{2000} = 639.13
\]
Rounded to two decimal places, the expected frequency is **639.13**.

#### 3. For **"Not Colorblind - Miss"**:
\[
\text{Expected Frequency (Not Colorblind - Miss)} = \frac{(1808 \times 291)}{2000} = \frac{526728}{2000} = 263.36
\]
Rounded to two decimal places, the expected frequency is **263.36**.

### Step 3: Complete the table
Now, we can fill in the table:

| Trial Outcome         | Hit   | Miss   | False Alarm | Correct Rejection | Total |
|-----------------------|-------|--------|-------------|-------------------|-------|
| **Colorblind**         | 77    | 22     | 23          | **67.97**          | 192   |
| **Not Colorblind**     | **639.13** | **263.36** | 271         | 638               | 1808  |
| **Total**              | 707   | 291    | 294         | 708               | 2000  |

The blanks have been filled with the expected frequencies rounded to two decimal places.

Would you like any further clarifications or details?

---

Here are 5 related questions to explore this topic further:

1. How do you interpret expected frequencies in a contingency table?
2. What is the chi-square test for independence, and how is it related to this problem?
3. How would you calculate the chi-square statistic based on observed and expected frequencies?
4. What are the conditions for using a chi-square test on categorical data?
5. How does the concept of statistical independence apply in the context of contingency tables?

**Tip:** When using contingency tables, always check if the row totals, column totals, and grand total match the original data to ensure accuracy in your calculations!

The following contingency table gives a summary of the data from 2000 trials of a visual experiment. Each of the trials was classified according to two variables: color vision of the participant ('Colorblind' or 'Not colorblind') and trial outcome ('Hit', 'Miss', 'False alarm', or 'Correct rejection'). 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, color vision of participant and trial outcome, are independent. Round your answers to two or more decimal places.

Solve a contingency table problem involving 2000 trials in a visual experiment, determining expected frequencies under the assumption of statistical independence. This problem covers key concepts like expected frequencies, probability, and chi-square test application. Ideal for college-level statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation