A summer intern at the Lego factory in Billund, Denmark, samples 41 yellow bricks and 35 red bricks and measures their weight. She finds sample means of 4.1 grams (yellow bricks) and 4.2 grams (red bricks), and sample standard deviations of 0.15 (yellow) and 0.23 (red), respectively. Compute the 75% confidence interval for the mean weight of red bricks. lower bound upper bound lower bound upper bound Compute the 75% confidence interval for the difference between the mean weights (i.e., red minus yellow). Hint: Compute the number of degrees of freedom, v, using Equation 5.20 in Chapter 5.6 4.156 lower bound 4.244 upper bound 4.09986 Compute the 75% confidence interval for the variance of the weight for the yellow bricks. 4.20014 4.12305 ? 4.17695 ? ? ? ?

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A summer intern at the Lego factory in Billund, Denmark, samples 41 yellow bricks and 35 red bricks and measures their weight. The sample means are 4.1 grams for yellow bricks and 4.2 grams for red bricks. The sample standard deviations are 0.15 grams for yellow bricks and 0.23 grams for red bricks, respectively.

1. **Confidence Interval for Mean Weight of Red Bricks:**
   - **Lower Bound:** 4.156 grams
   - **Upper Bound:** 4.244 grams

2. **Confidence Interval for the Difference in Mean Weights (Red Minus Yellow):**
   - **Lower Bound:** 4.09986 grams
   - **Upper Bound:** 4.20014 grams
   - **Hint:** Compute the degrees of freedom using Equation 5.20 in Chapter 5.6.

3. **Confidence Interval for the Variance of Weight for Yellow Bricks:**
   - **Lower Bound:** 4.12305
   - **Upper Bound:** 4.17695

These intervals estimate the range within which the true mean or variance is expected to lie with 75% confidence.
Transcribed Image Text:A summer intern at the Lego factory in Billund, Denmark, samples 41 yellow bricks and 35 red bricks and measures their weight. The sample means are 4.1 grams for yellow bricks and 4.2 grams for red bricks. The sample standard deviations are 0.15 grams for yellow bricks and 0.23 grams for red bricks, respectively. 1. **Confidence Interval for Mean Weight of Red Bricks:** - **Lower Bound:** 4.156 grams - **Upper Bound:** 4.244 grams 2. **Confidence Interval for the Difference in Mean Weights (Red Minus Yellow):** - **Lower Bound:** 4.09986 grams - **Upper Bound:** 4.20014 grams - **Hint:** Compute the degrees of freedom using Equation 5.20 in Chapter 5.6. 3. **Confidence Interval for the Variance of Weight for Yellow Bricks:** - **Lower Bound:** 4.12305 - **Upper Bound:** 4.17695 These intervals estimate the range within which the true mean or variance is expected to lie with 75% confidence.
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