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Indicate whether 25 is sufficient or whether a sample of 50 would be necessary. You will want to calculate the probability of the sample mean being between $11,000 and $13,000 for both a sample size of 25 and 50. (Thank You!)

Indicate whether 25 is sufficient or whether a sample of 50 would be necessary. You will want to calculate the probability of the sample mean being between $11,000 and $13,000 for both a sample size of 25 and 50. (Thank You!)

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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Indicate whether 25 is sufficient or whether a sample of 50 would be necessary. You will want to calculate the probability of the sample mean being between $11,000 and $13,000 for both a sample size of 25 and 50.

(Thank You!)

**Title: Importance of Sampling in Client Feedback Collection** **Letter from Robin Banks to Assistant Manager** **Context:** The company is committed to providing exceptional service by thoroughly understanding its clients. An initiative is underway to collect feedback via phone calls from a representative sample of clients due to the practical constraints of reaching all 10,000 clients. **Key Details:** - **Client Base:** 10,000 clients. - **Average Account Balance:** $12,000. - **Standard Deviation:** $5,000. - **Sampling Goal:** Select a sample size that ensures at least an 80% probability that the sample mean is within $1,000 of the overall client mean. **Inquiry:** - Consider a random sample size of either 25 or 50 clients. - Which sample size will likely achieve the desired probability? **Request for Action:** The letter emphasizes the importance of using statistical expertise to determine an appropriate sample size efficiently. Quick feedback is solicited to proceed with the sampling strategy. **Conclusion:** Sampling not only saves time and resources but also provides statistically significant insights into the client base when properly executed. The choice between sample sizes is critical to ensure the reliability and validity of the resulting data.
Transcribed Image Text:**Title: Importance of Sampling in Client Feedback Collection** **Letter from Robin Banks to Assistant Manager** **Context:** The company is committed to providing exceptional service by thoroughly understanding its clients. An initiative is underway to collect feedback via phone calls from a representative sample of clients due to the practical constraints of reaching all 10,000 clients. **Key Details:** - **Client Base:** 10,000 clients. - **Average Account Balance:** $12,000. - **Standard Deviation:** $5,000. - **Sampling Goal:** Select a sample size that ensures at least an 80% probability that the sample mean is within $1,000 of the overall client mean. **Inquiry:** - Consider a random sample size of either 25 or 50 clients. - Which sample size will likely achieve the desired probability? **Request for Action:** The letter emphasizes the importance of using statistical expertise to determine an appropriate sample size efficiently. Quick feedback is solicited to proceed with the sampling strategy. **Conclusion:** Sampling not only saves time and resources but also provides statistically significant insights into the client base when properly executed. The choice between sample sizes is critical to ensure the reliability and validity of the resulting data.
Expert Solution
Step 1

Population mean, μ = 12000

Population standard deviation  ,σ = 5000

Confidence level = 0.8

Significance level = 0.2

Margin of Error= ME = 1000

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