Question
fuction to Statistics Adilene Molina \( 02 / 02 / 2511: 3 \) s of Relative Standing Question 3, 3.3.9 HW score: \( 62.98 \%, 8.82 \) of 14 points Part 1 of 2 Points: 0 of 1 e the range rule of thumb to identify the values that are significantly low, the values that are significantly high, and the values that are neither significantly low nor significantly high. est is used to assess readiness for college. In a recent year, the mean test score was 21.5 and the standard deviation was 4.6 . Identify the test scores that are significantly low or significantly high at test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
Ask by Bolton Burns. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Significantly low test scores are below 12.3, significantly high scores are above 30.7, and scores between 12.3 and 30.7 are neither significantly low nor high.
Solution
Sure, let's use the **range rule of thumb** to determine which test scores are significantly low or significantly high based on the given data.
### **Given:**
- **Mean (μ):** 21.5
- **Standard Deviation (σ):** 4.6
### **Range Rule of Thumb:**
This rule states that:
- **Significantly Low:** Scores **more than 2 standard deviations below** the mean.
- **Significantly High:** Scores **more than 2 standard deviations above** the mean.
- **Neither:** Scores within **2 standard deviations** of the mean.
### **Calculations:**
1. **Calculate 2 Standard Deviations:**
\[
2σ = 2 \times 4.6 = 9.2
\]
2. **Determine Thresholds:**
- **Significantly Low Threshold:**
\[
\text{Mean} - 2σ = 21.5 - 9.2 = 12.3
\]
So, any score **below 12.3** is **significantly low**.
- **Significantly High Threshold:**
\[
\text{Mean} + 2σ = 21.5 + 9.2 = 30.7
\]
So, any score **above 30.7** is **significantly high**.
3. **Interpretation:**
- **Significantly Low Scores:** **< 12.3**
- **Significantly High Scores:** **> 30.7**
- **Neither Significantly Low nor High:** **12.3 ≤ score ≤ 30.7**
### **Summary:**
- **Significantly Low:** Any test score **less than 12.3**.
- **Significantly High:** Any test score **greater than 30.7**.
- **Neither:** Any test score **between 12.3 and 30.7** (inclusive).
### **Answer:**
- **Significantly low** test scores are **below 12.3**.
- **Significantly high** test scores are **above 30.7**.
- Test scores between **12.3 and 30.7** are **neither significantly low nor high**.
If you need to fill in specific blanks or select from multiple-choice options, use **12.3** as the lower threshold and **30.7** as the upper threshold based on the range rule of thumb.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To determine significantly low and high test scores using the range rule of thumb, we apply the mean and standard deviation. In this case, scores are significantly low if they are more than 2 standard deviations below the mean. Therefore, we calculate \(21.5 - 2(4.6) = 12.3\). Any score below 12.3 is considered significantly low! Conversely, scores are significantly high if they exceed 2 standard deviations above the mean, calculated as \(21.5 + 2(4.6) = 30.7\). Any score above 30.7 is regarded as significantly high! So, scores below 12.3 are low and those above 30.7 are high. Students, don't leave those scores hanging in the balance!
