A researcher records the repair cost for 4 randomly selected refrigerators. A sample mean of $85.03 and standard deviation of $22.34 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.
A researcher records the repair cost for 4 randomly selected refrigerators. A sample mean of $85.03 and standard deviation of $22.34 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.
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#35 steps 1 and 2
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**MAT 106.04 Professor Felix**
Page 131 of 135](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc019303-f71f-44c9-a166-98b7cccf70ca%2F7fa4d16c-8a18-4a1d-8c38-a45571dd20bc%2Fygxa3we_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Confidence Interval Calculation for Mean Repair Cost
#### Step 2: Selecting the \( t \) Value from the \( t \) Table
Assuming the degrees of freedom equals 10, select the \( t \) value from the \( t \) table.
**Answer:**
#### Problem 35
A researcher records the repair cost for 4 randomly selected refrigerators. A sample mean of $85.03 and standard deviation of $22.34 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.
#### Step 1: Find the Critical Value
Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
**Answer:**
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#### Visual Explanations
The text includes four normal distribution graphs as follows:
1. **Graph 1:**
- Horizontal axis marked with "0" and "t = ?"
- Represents understanding the critical value without a specified \( t \) value.
2. **Graph 2:**
- Horizontal axis marked with "t = ?" and "0"
- Reflects the consideration of the critical region with unknown \( t \).
3. **Graph 3:**
- Horizontal axis marked with "-t = ?" and "0"
- Similar to the first and second, emphasizing the symmetrical nature of the t-distribution for critical values both positive and negative.
4. **Graph 4:**
- Horizontal axis marked with "-t = ?" and "0"
- Illustrates the complete understanding once the correct critical value \( t \) is determined in context to degrees of freedom.
---
For more resources and detailed walkthroughs, visit [Our Educational Website](#).
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**MAT 106.04 Professor Felix**
Page 131 of 135
![### Step 2: Construct the 80% Confidence Interval
Construct the 80% confidence interval. Round your answer to two decimal places.
**Answer:**
- Lower endpoint: _______________
- Upper endpoint: _______________
### 36. Estimating the Fraction of Tenth Grade Students' Reading Skills
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.02? Round your answer up to the next integer.
**Answer:** _______________
### 37. Sample of Full Size Down Comforters
In a sample of 34 full size down comforters, the average weight was found to be 34.5 ounces with a variance of 2.6.
Give a point estimate for the population variance of the weight of the full size down comforters. Round your answer to two decimal places, if necessary.
**Answer:** _______________
### 38. Difference Between Population Means
Find the point estimate for the true difference between the given population means. Round your answer to the nearest whole number.
\[
\bar{x}_1 = 50 \quad \text{and} \quad \bar{x}_2 = 39
\]
**Answer:** _______________](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc019303-f71f-44c9-a166-98b7cccf70ca%2F7fa4d16c-8a18-4a1d-8c38-a45571dd20bc%2Fu0jky4d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Step 2: Construct the 80% Confidence Interval
Construct the 80% confidence interval. Round your answer to two decimal places.
**Answer:**
- Lower endpoint: _______________
- Upper endpoint: _______________
### 36. Estimating the Fraction of Tenth Grade Students' Reading Skills
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.02? Round your answer up to the next integer.
**Answer:** _______________
### 37. Sample of Full Size Down Comforters
In a sample of 34 full size down comforters, the average weight was found to be 34.5 ounces with a variance of 2.6.
Give a point estimate for the population variance of the weight of the full size down comforters. Round your answer to two decimal places, if necessary.
**Answer:** _______________
### 38. Difference Between Population Means
Find the point estimate for the true difference between the given population means. Round your answer to the nearest whole number.
\[
\bar{x}_1 = 50 \quad \text{and} \quad \bar{x}_2 = 39
\]
**Answer:** _______________
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