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Suppose you take two SRS from a large population, one of size 800 and one of size 300. If you use these data to construct a 99% confidence interval for u, which will have the smaller margin of error? The sample of size 800 The sample of size 300 They will be about the same

Suppose you take two SRS from a large population, one of size 800 and one of size 300. If you use these data to construct a 99% confidence interval for u, which will have the smaller margin of error? The sample of size 800 The sample of size 300 They will be about the same

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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**Statistical Analysis: Understanding Margin of Error** **Scenario:** Suppose you take two Simple Random Samples (SRS) from a large population: one sample of size 800 and one sample of size 300. If you use these data to construct a 99% confidence interval for the population mean (μ), which sample will have the smaller margin of error? **Choices:** - ☐ The sample of size 800 - ☑ The sample of size 300 - ☐ They will be about the same **Explanation:** In general, for a given confidence level, the margin of error is inversely proportional to the square root of the sample size. Hence, a larger sample size results in a smaller margin of error. Therefore, the sample of size 800 will have a smaller margin of error compared to the sample of size 300.
Transcribed Image Text:**Statistical Analysis: Understanding Margin of Error** **Scenario:** Suppose you take two Simple Random Samples (SRS) from a large population: one sample of size 800 and one sample of size 300. If you use these data to construct a 99% confidence interval for the population mean (μ), which sample will have the smaller margin of error? **Choices:** - ☐ The sample of size 800 - ☑ The sample of size 300 - ☐ They will be about the same **Explanation:** In general, for a given confidence level, the margin of error is inversely proportional to the square root of the sample size. Hence, a larger sample size results in a smaller margin of error. Therefore, the sample of size 800 will have a smaller margin of error compared to the sample of size 300.
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