Is there a significant difference between how people study in college? College students tend to have different ways of studying for their classes. A sociology student, Linus, decided to investigate three common study methods: alone, with friends, and with a tutor. To do this, Linus surveyed a random sample of students, asking them how much time (in hours) in a given week they would spend studying based on each method.
Studying Alone	Studying with Friends	Studying with a Tutor
13	11	5
13	16	2
9	8	5
16	7	1
21	1	0
18	0	3
20	4	4
21
SSTOT =1086, SSBET = 735.839, Find SSW and check that SSTOT = SSBET + SSW. (Round your answer to three decimal places.)
SSW =

To solve this, we need to calculate **SSW** (Sum of Squares Within), which represents the variation within each group in the study (i.e., the variance in study hours within the three methods).

Given that the **SSTOT** (Total Sum of Squares) and **SSBET** (Sum of Squares Between) are provided, we can find **SSW** using the formula:

\[
SSW = SSTOT - SSBET
\]

### Step 1: Substitute the given values
We are given:

- **SSTOT** = 1086
- **SSBET** = 735.839

Now calculate **SSW**:

\[
SSW = 1086 - 735.839
\]

\[
SSW = 350.161
\]

### Conclusion:
\[
SSW = 350.161
\]

This satisfies the condition that:
\[
SSTOT = SSBET + SSW
\]
\[
1086 = 735.839 + 350.161
\]

The equation holds true. Therefore, the value of **SSW** is **350.161** (rounded to three decimal places).

Would you like more details about how these sums of squares are calculated or any further questions about this process?

---

Here are five relative questions:
1. How do you compute the Sum of Squares Between (SSBET)?
2. What is the purpose of calculating the Sum of Squares Within (SSW)?
3. How does the Analysis of Variance (ANOVA) use SSTOT, SSBET, and SSW?
4. Can you explain the difference between variance within groups and variance between groups?
5. How would you interpret the significance of this test based on the SSW value?

**Tip**: When performing statistical analyses, always verify that the sums of squares add up correctly, as it's a key step to ensure consistency in your calculations.

Is there a significant difference between how people study in college? College students tend to have different ways of studying for their classes. A sociology student, Linus, decided to investigate three common study methods: alone, with friends, and with a tutor. To do this, Linus surveyed a random sample of students, asking them how much time (in hours) in a given week they would spend studying based on each method. Studying Alone: 13, 13, 9, 16, 21, 18, 20, 21; Studying with Friends: 11, 16, 8, 7, 1, 0, 4; Studying with a Tutor: 5, 2, 5, 1, 0, 3, 4. SSTOT = 1086, SSBET = 735.839, Find SSW and check that SSTOT = SSBET + SSW. (Round your answer to three decimal places.)

Explore how to calculate the Sum of Squares Within (SSW) using the ANOVA method with given SSTOT (1086) and SSBET (735.839). This example involves a college-level study comparing study methods (alone, with friends, and with a tutor) based on hours studied. Learn the key formulas for SSW and SSTOT verification.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation