Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
1. Intro to Stats and Collecting Data
Intro to Stats
Problem 1.3.8b
Textbook Question
Sampling Method Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type.
b. Systematic sample

1
Identify the total number of students in your statistics class, which will be the population size (N).
Determine the sample size you need, which in this case is six students.
Calculate the sampling interval (k) by dividing the population size (N) by the sample size (n). Use the formula: . Round down to the nearest whole number if necessary.
Select a random starting point from the first k students. This can be done by using a random number generator to pick a number between 1 and k.
Select every k-th student from the starting point to form your sample of six students. Continue this process until you have selected all six students.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Systematic Sampling
Systematic sampling is a method where you select every k-th element from a list or sequence. To implement this, you first determine the sampling interval k by dividing the population size by the desired sample size. Then, you randomly select a starting point within the first k elements and continue selecting every k-th element thereafter to form your sample.
Recommended video:
Sampling Distribution of Sample Proportion
Population and Sample
In statistics, the population refers to the entire group of individuals or instances about whom we want to draw conclusions, while a sample is a subset of the population that is used to represent the whole. In this context, the population is all students in the statistics class, and the sample is the six students selected using the systematic sampling method.
Recommended video:
Sampling Distribution of Sample Proportion
Random Start
A random start is crucial in systematic sampling to ensure that the sample is unbiased and representative of the population. This involves randomly selecting a starting point within the first k elements of the population list, which helps in avoiding any periodic patterns that might exist in the population data, thus maintaining the randomness of the sample.
Recommended video:
Guided course
Intro to Random Variables & Probability Distributions
Watch next
Master Introduction to Statistics Channel with a bite sized video explanation from Patrick
Start learning