Question Help▼ ¤ SCO The ages of a group of 155 randomly selected adult females have a standard deviation of 16.6 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let o = 16.6 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 90% 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 ages of females in the general population? The required sample size is (Round up to the nearest whole number as needed.) Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? O A. Yes, because statistics students are typically younger than people in the general population. OB. No, because there is no age difference between the population of statistics students and the general population. O C. Yes, because statistics students are typically older than people in the general population. OD. No, because statistics students are typically older than people in the general population. ScO SCO Click to select your answer(s).
Question Help▼ ¤ SCO The ages of a group of 155 randomly selected adult females have a standard deviation of 16.6 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let o = 16.6 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 90% 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 ages of females in the general population? The required sample size is (Round up to the nearest whole number as needed.) Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? O A. Yes, because statistics students are typically younger than people in the general population. OB. No, because there is no age difference between the population of statistics students and the general population. O C. Yes, because statistics students are typically older than people in the general population. OD. No, because statistics students are typically older than people in the general population. ScO SCO Click to select your answer(s).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Educational Resource: Understanding Sample Size Calculations**
In a statistical study, the ages of a group of 155 randomly selected adult females were found to have a standard deviation of 16.6 years. Let’s assume this standard deviation (\( \sigma \)) applies to the general population of females. For our calculations, we will use \( \sigma = 16.6 \) years.
The objective is to determine the number of female statistics students required to estimate the mean age of the entire population of female statistics students with a 90% confidence level, where the sample mean is within half a year of the true population mean.
**Steps to Calculate the Required Sample Size:**
1. **Identify Parameters**:
- Standard Deviation (\( \sigma \)): 16.6 years
- Desired Margin of Error (E): 0.5 year
- Confidence Level: 90%
2. **Z-Score for 90% Confidence Level**:
- The critical value (Z) for a 90% confidence level is typically 1.645.
3. **Formula for Sample Size (n)**:
\[
n = \left( \frac{Z \times \sigma}{E} \right)^2
\]
4. **Calculation**:
\[
n = \left( \frac{1.645 \times 16.6}{0.5} \right)^2
\]
\[
n \approx 2983.9056
\]
Rounding up to the nearest whole number, the required sample size is 2984.
**Required Sample Size is: 2984**
(Round up to the nearest whole number as needed.)
**Question: Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?**
**Possible Answers**:
- **A**. Yes, because statistics students are typically younger than people in the general population.
- **B**. No, because there is no age difference between the population of statistics students and the general population.
- **C**. Yes, because statistics students are typically older than people in the general population.
- **D**. No, because statistics students are typically older than people in the general population.
**[Click to select your answer(s)]**
---
This exercise demonstrates the importance of sample size in estimating population parameters accurately](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f4a9f05-fdd6-4e90-876c-ee547117be59%2Ffdc29a45-d79c-47f4-bb80-7102ffbab876%2Fl8pe67mv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Understanding Sample Size Calculations**
In a statistical study, the ages of a group of 155 randomly selected adult females were found to have a standard deviation of 16.6 years. Let’s assume this standard deviation (\( \sigma \)) applies to the general population of females. For our calculations, we will use \( \sigma = 16.6 \) years.
The objective is to determine the number of female statistics students required to estimate the mean age of the entire population of female statistics students with a 90% confidence level, where the sample mean is within half a year of the true population mean.
**Steps to Calculate the Required Sample Size:**
1. **Identify Parameters**:
- Standard Deviation (\( \sigma \)): 16.6 years
- Desired Margin of Error (E): 0.5 year
- Confidence Level: 90%
2. **Z-Score for 90% Confidence Level**:
- The critical value (Z) for a 90% confidence level is typically 1.645.
3. **Formula for Sample Size (n)**:
\[
n = \left( \frac{Z \times \sigma}{E} \right)^2
\]
4. **Calculation**:
\[
n = \left( \frac{1.645 \times 16.6}{0.5} \right)^2
\]
\[
n \approx 2983.9056
\]
Rounding up to the nearest whole number, the required sample size is 2984.
**Required Sample Size is: 2984**
(Round up to the nearest whole number as needed.)
**Question: Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?**
**Possible Answers**:
- **A**. Yes, because statistics students are typically younger than people in the general population.
- **B**. No, because there is no age difference between the population of statistics students and the general population.
- **C**. Yes, because statistics students are typically older than people in the general population.
- **D**. No, because statistics students are typically older than people in the general population.
**[Click to select your answer(s)]**
---
This exercise demonstrates the importance of sample size in estimating population parameters accurately
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman