Need help with first 3 sections of questions ### Assessing Sample Variance in Ball Bearings ManufacturePart variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wearout. Production standards call for a maximum variance of $0.0001$ when the bearing sizes are measured in inches. A sample of $11$ bearings shows a sample standard deviation of $0.015$ inches.**Problem Statement:**1. **Hypothesis Testing:** - **Objective:** To determine whether the sample indicates that the maximum acceptable variance is being exceeded using $\alpha = 0.10$. - **Null Hypothesis ($H_0$):** \[ \sigma^2 \leq 0.0001 \] - **Alternative Hypothesis ($H_a$):** \[ \sigma^2 > 0.0001 \] **Task:** 1. Calculate the value of the test statistic (to 2 decimals). 2. Determine the p-value. 3. Draw a conclusion regarding the variance surpassing the maximum requirement.2. **Confidence Interval:** - **Objective:** Compute the $90\%$ confidence interval estimate of the variance of the ball bearings in the population (to 5 decimals). \[ \text{Confidence Interval: } \leq \sigma^2 \leq \]**Instructions:**1. Fill in the selections and calculations accurately: - Select your conclusion from the given options. - Compute the test statistic and p-value. - Derive the confidence interval estimate. The proper conduct of hypothesis testing and interval estimation will help in quality control ensuring that the variances of ball bearings stay within acceptable limits enhancing reliability and performance of the products.

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Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rap wearout. Production standards call for a maximum variance of 0.0001 when the bearing sizes are measured in inches. A sample of 11 bear shows a sample standard deviation of 0.015 inches.

Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rap wearout. Production standards call for a maximum variance of 0.0001 when the bearing sizes are measured in inches. A sample of 11 bear shows a sample standard deviation of 0.015 inches.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Need help with first 3 sections of questions

### Assessing Sample Variance in Ball Bearings Manufacture

Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wearout. Production standards call for a maximum variance of $0.0001$ when the bearing sizes are measured in inches. A sample of $11$ bearings shows a sample standard deviation of $0.015$ inches.

**Problem Statement:**

1. **Hypothesis Testing:**
- **Objective:** To determine whether the sample indicates that the maximum acceptable variance is being exceeded using $\alpha = 0.10$.
- **Null Hypothesis ($H_0$):**
\[
\sigma^2 \leq 0.0001
\]
- **Alternative Hypothesis ($H_a$):**
\[
\sigma^2 > 0.0001
\]

**Task:**
1. Calculate the value of the test statistic (to 2 decimals).
2. Determine the p-value.
3. Draw a conclusion regarding the variance surpassing the maximum requirement.

2. **Confidence Interval:**
- **Objective:** Compute the $90\%$ confidence interval estimate of the variance of the ball bearings in the population (to 5 decimals).
\[
\text{Confidence Interval: } \leq \sigma^2 \leq
\]

**Instructions:**

1. Fill in the selections and calculations accurately:
- Select your conclusion from the given options.
- Compute the test statistic and p-value.
- Derive the confidence interval estimate.

The proper conduct of hypothesis testing and interval estimation will help in quality control ensuring that the variances of ball bearings stay within acceptable limits enhancing reliability and performance of the products.

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