**Sample Size Calculations and Confidence Intervals** **13. Basic Computation: Sample Size** Suppose \( x \) has a mound-shaped distribution with \( \sigma = 3 \). - (a) Find the minimal sample size required so that for a 95% confidence interval, the maximal margin of error is \( E = 0.4 \). - (b) Check Requirements: Based on this sample size, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **14. Basic Computation: Sample Size** Suppose \( x \) has a normal distribution with \( \sigma = 1.2 \). - (a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is \( E = 0.5 \). - (b) Check Requirements: Based on this sample size and the \( \bar{x} \) distribution, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **15. Zoology: Hummingbirds** Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther (Reference: *Hummingbirds* by K. Long and W. Alther). A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is \( \bar{x} = 3.15 \) grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds are normally distributed, with \( \sigma = 0.33 \) gram. - (a) Find an 80% confidence interval for the average weight of Allen’s hummingbirds in the study region. What is the margin of error? - (b) What conditions are necessary for your calculations? - (c) Interpret: Compare your results in the context of this problem. - (d) Sample Size: Find the sample size necessary for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weight of the hummingbirds. **16. Diagnostic Tests: Uric Acid** Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma (Reference: *A Manual of Laboratory and Diagnostic Tests* by F. Fischbach).
**Sample Size Calculations and Confidence Intervals** **13. Basic Computation: Sample Size** Suppose \( x \) has a mound-shaped distribution with \( \sigma = 3 \). - (a) Find the minimal sample size required so that for a 95% confidence interval, the maximal margin of error is \( E = 0.4 \). - (b) Check Requirements: Based on this sample size, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **14. Basic Computation: Sample Size** Suppose \( x \) has a normal distribution with \( \sigma = 1.2 \). - (a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is \( E = 0.5 \). - (b) Check Requirements: Based on this sample size and the \( \bar{x} \) distribution, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain. **15. Zoology: Hummingbirds** Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther (Reference: *Hummingbirds* by K. Long and W. Alther). A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is \( \bar{x} = 3.15 \) grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds are normally distributed, with \( \sigma = 0.33 \) gram. - (a) Find an 80% confidence interval for the average weight of Allen’s hummingbirds in the study region. What is the margin of error? - (b) What conditions are necessary for your calculations? - (c) Interpret: Compare your results in the context of this problem. - (d) Sample Size: Find the sample size necessary for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weight of the hummingbirds. **16. Diagnostic Tests: Uric Acid** Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma (Reference: *A Manual of Laboratory and Diagnostic Tests* by F. Fischbach).
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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How to solve problems 13-16 ?
Transcribed Image Text:**Sample Size Calculations and Confidence Intervals**
**13. Basic Computation: Sample Size**
Suppose \( x \) has a mound-shaped distribution with \( \sigma = 3 \).
- (a) Find the minimal sample size required so that for a 95% confidence interval, the maximal margin of error is \( E = 0.4 \).
- (b) Check Requirements: Based on this sample size, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain.
**14. Basic Computation: Sample Size**
Suppose \( x \) has a normal distribution with \( \sigma = 1.2 \).
- (a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is \( E = 0.5 \).
- (b) Check Requirements: Based on this sample size and the \( \bar{x} \) distribution, can we assume that the \( \bar{x} \) distribution is approximately normal? Explain.
**15. Zoology: Hummingbirds**
Allen’s hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther (Reference: *Hummingbirds* by K. Long and W. Alther). A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is \( \bar{x} = 3.15 \) grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds are normally distributed, with \( \sigma = 0.33 \) gram.
- (a) Find an 80% confidence interval for the average weight of Allen’s hummingbirds in the study region. What is the margin of error?
- (b) What conditions are necessary for your calculations?
- (c) Interpret: Compare your results in the context of this problem.
- (d) Sample Size: Find the sample size necessary for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weight of the hummingbirds.
**16. Diagnostic Tests: Uric Acid**
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma (Reference: *A Manual of Laboratory and Diagnostic Tests* by F. Fischbach).
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