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Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.76. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.) 5.19 4.51 (₁ (b) Compute a 98% CI for true average porosity of another seam based on 15 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) ✓ , 5.02 4.10 (c) How large a sample size is necessary if the width of the 95% interval is to be 0.36? (Round your answer up to the nearest whole number.) 69 specimens (d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.76. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.) 5.19 4.51 (₁ (b) Compute a 98% CI for true average porosity of another seam based on 15 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) ✓ , 5.02 4.10 (c) How large a sample size is necessary if the width of the 95% interval is to be 0.36? (Round your answer up to the nearest whole number.) 69 specimens (d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.76. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.) \[ (4.51, 5.19) \] (b) Compute a 98% CI for true average porosity of another seam based on 15 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) \[ (4.10, 5.02) \] (c) How large a sample size is necessary if the width of the 95% interval is to be 0.36? (Round your answer up to the nearest whole number.) \[ 69 \text{ specimens} \] (d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.) \[ \text{specimens} \]
Transcribed Image Text:Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.76. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.) \[ (4.51, 5.19) \] (b) Compute a 98% CI for true average porosity of another seam based on 15 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) \[ (4.10, 5.02) \] (c) How large a sample size is necessary if the width of the 95% interval is to be 0.36? (Round your answer up to the nearest whole number.) \[ 69 \text{ specimens} \] (d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.) \[ \text{specimens} \]
## Survey Sample Size Calculation for Electorate Awareness A state legislator intends to survey her district's residents to determine the proportion aware of her stance on using state funds for abortions. The required sample size calculations are detailed below. ### Task: Determine Necessary Sample Size To ensure the 95% confidence interval (CI) for the proportion (p) has a maximum width of 0.11, we perform the following calculations: #### (a) General Sample Size Requirement - **Question:** What sample size is necessary if the 95% CI for \( p \) is to have a width of at most 0.11, irrespective of \( p \)? - **Answer:** A sample size of **318 people** is required. #### (b) Sample Size with Prior Knowledge - **Scenario:** The legislator believes that at least \( \frac{6}{7} \) of the electorate are aware of her position. - **Question:** How large a sample size is needed to maintain a width of at most 0.11? - **Answer:** A sample size of **156 people** is recommended. ### Notes For detailed calculations, refer to the appropriate table in the [Appendix of Tables](#). This appendix aids in determining the critical values and necessary adjustments for confidence interval width calculations.
Transcribed Image Text:## Survey Sample Size Calculation for Electorate Awareness A state legislator intends to survey her district's residents to determine the proportion aware of her stance on using state funds for abortions. The required sample size calculations are detailed below. ### Task: Determine Necessary Sample Size To ensure the 95% confidence interval (CI) for the proportion (p) has a maximum width of 0.11, we perform the following calculations: #### (a) General Sample Size Requirement - **Question:** What sample size is necessary if the 95% CI for \( p \) is to have a width of at most 0.11, irrespective of \( p \)? - **Answer:** A sample size of **318 people** is required. #### (b) Sample Size with Prior Knowledge - **Scenario:** The legislator believes that at least \( \frac{6}{7} \) of the electorate are aware of her position. - **Question:** How large a sample size is needed to maintain a width of at most 0.11? - **Answer:** A sample size of **156 people** is recommended. ### Notes For detailed calculations, refer to the appropriate table in the [Appendix of Tables](#). This appendix aids in determining the critical values and necessary adjustments for confidence interval width calculations.
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