## Estimating Sample Size for Female Statistics Students**Scenario Description:** The ages of a group of 131 randomly selected adult females have a standard deviation of 16.4 years. Assume that the ages of female statistics students have less variation than the ages of females in the general population, so let σ = 16.4 years for the sample size calculation. How many female statistics students' ages must be obtained to estimate the mean age of all female statistics students?Assume that we want 95% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than the ages of females in the general population?**Calculation Section:**- **Population Standard Deviation (σ):** 16.4 years- **Desired Margin of Error:** 0.5 years- **Confidence Level:** 95%**Sample Size Calculation:**To calculate the required sample size, use the formula for sample size calculation in estimating a population mean with a given confidence level and margin of error:\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]Where:- \( Z \) is the Z-value corresponding to the desired confidence level (for 95% confidence, \( Z \approx 1.96 \))- \( \sigma \) is the population standard deviation- \( E \) is the desired margin of errorThe required sample size is: **\[ \boxed{} \]***(Round up to the nearest whole number as needed.)***Reasonability Check:**Does it seem reasonable to assume that the ages of female statistics students have less variation than the ages of females in the general population?**Possible Responses:**- A. Yes, because statistics students are typically younger than people in the general population.- B. No, because statistics students are typically older than people in the general population.- C. No, because there is no age difference between the population of statistics students and the general population.- D. Yes, because statistics students are typically older than people in the general population.Choose the most appropriate response based on your understanding and reasoning.

Name: ## Estimating Sample Size for Female Statistics Students**Scenario De
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ## Estimating Sample Size for Female Statistics Students**Scenario Description:** The ages of a group of 131 randomly selected adult females have a standard deviation of 16.4 years. Assume that the ages of female statistics students have less varia