Question
Suppose the size of a population is \( \mathrm{N}=2500 \) and the sample size desired is \( \mathrm{n}=15 \). What value of k should be used to obtain a systematic sample from this population? \( k=\square \) (Round down to the nearest whole number as needed.)
Ask by Haynes Phillips. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( k = 166 \)
Solution
To obtain a systematic sample, you need to determine the step size \( k \) by dividing the population size \( \mathrm{N} \) by the desired sample size \( \mathrm{n} \). The formula is:
\[
k = \left\lfloor \frac{\mathrm{N}}{\mathrm{n}} \right\rfloor
\]
Given:
- Population size \( \mathrm{N} = 2500 \)
- Desired sample size \( \mathrm{n} = 15 \)
Calculate \( k \):
\[
k = \left\lfloor \frac{2500}{15} \right\rfloor = \left\lfloor 166.666\ldots \right\rfloor = 166
\]
**Answer:**
\( k = 166 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the value of \( k \) for systematic sampling, you can use the formula \( k = \frac{N}{n} \), where \( N \) is the population size and \( n \) is the sample size. So, substituting the values you provided, we have: \[ k = \frac{2500}{15} \approx 166.67 \] Rounding down to the nearest whole number gives us \( k = 166 \). Thus, you would select every 166th individual from the population to create your sample. Happy sampling!
