The ages of a group of 133 randomly selected adult females have a standard deviation of 18.6 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so et o = 18.6 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 98% 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. O B. Yes, because statistics students are typically older than people in the general population. O C. No, because there is no age difference between the population of statistics students and the general population. O D. No, because statistics students are typically older than people in the general population.
The ages of a group of 133 randomly selected adult females have a standard deviation of 18.6 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so et o = 18.6 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 98% 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. O B. Yes, because statistics students are typically older than people in the general population. O C. No, because there is no age difference between the population of statistics students and the general population. O D. No, because statistics students are typically older than people in the general population.
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![### Determining Sample Size for Female Statistics Students' Ages
The ages of a group of 133 randomly selected adult females have a standard deviation of 18.6 years. Assume that the ages of female statistics students have less variation than the ages of females in the general population, so let \(\sigma = 18.6\) 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 98% 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?
#### Sample Size Calculation
The required sample size is \[\_\_\_\_].
(Round up to the nearest whole number as needed.)
#### Assessing Reasonableness
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?
- A. Yes, because statistics students are typically younger than people in the general population.
- B. Yes, 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. No, because statistics students are typically older than people in the general population.
### Understanding the Context
To determine the necessary sample size, one typically uses the formula for the sample size needed for estimating a population mean:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( n \) is the sample size.
- \( Z_{\alpha/2} \) is the Z-score corresponding to the desired confidence level (for 98%, \( Z_{\alpha/2} \approx 2.33 \)).
- \( \sigma \) is the population standard deviation (18.6 years in this context).
- \( E \) is the margin of error (0.5 years in this context).
Thus, in order to calculate the sample size:
1. Plug in the values:
\[ n = \left( \frac{2.33 \cdot 18.6}{0.5} \right)^2 \]
2. Simplify the computations to find \( n \).
Rounding up the final result gives the required sample size](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86445a01-0a3f-49cc-9d22-b352e3028fb5%2F005bc6f7-42d3-4058-8d2d-ea86a5bbdcc6%2Fuf9enhp_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Sample Size for Female Statistics Students' Ages
The ages of a group of 133 randomly selected adult females have a standard deviation of 18.6 years. Assume that the ages of female statistics students have less variation than the ages of females in the general population, so let \(\sigma = 18.6\) 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 98% 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?
#### Sample Size Calculation
The required sample size is \[\_\_\_\_].
(Round up to the nearest whole number as needed.)
#### Assessing Reasonableness
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?
- A. Yes, because statistics students are typically younger than people in the general population.
- B. Yes, 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. No, because statistics students are typically older than people in the general population.
### Understanding the Context
To determine the necessary sample size, one typically uses the formula for the sample size needed for estimating a population mean:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( n \) is the sample size.
- \( Z_{\alpha/2} \) is the Z-score corresponding to the desired confidence level (for 98%, \( Z_{\alpha/2} \approx 2.33 \)).
- \( \sigma \) is the population standard deviation (18.6 years in this context).
- \( E \) is the margin of error (0.5 years in this context).
Thus, in order to calculate the sample size:
1. Plug in the values:
\[ n = \left( \frac{2.33 \cdot 18.6}{0.5} \right)^2 \]
2. Simplify the computations to find \( n \).
Rounding up the final result gives the required sample size
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