Here is the solution to the questions presented in the image:

(i) What will the sample size be?

The sample size is determined by the interval provided, which is every 50th student. Since there are 5,000 students:

$\text{Sample Size} = \frac{\text{Total Students}}{\text{Interval}} = \frac{5000}{50} = 100$

Answer: The sample size will be 100.

(ii) Is this a probability or non-probability sampling method? Identify the sampling technique.

This is a probability sampling method because every student in the population has an equal chance of being selected. The technique used is systematic sampling, where a random starting point is chosen, and every 50th student is selected thereafter.

Answer: It is a probability sampling method using the systematic sampling technique.

(iii) If the list is not alphabetical but is ordered by students’ scores in the previous semester, would this sampling method be sufficient?

If the list is ordered by students' scores, the systematic sampling might introduce bias. For example, students with similar scores (e.g., high achievers) could be disproportionately included in or excluded from the sample, making it less representative of the overall population.

Answer: The sampling method would not be sufficient because ordering by scores could create bias, making the sample non-representative of the population.

(iv) If one decides to take the first hundred students on campus streets as the sample, will that be a non-probability method? What sampling method will that be?

Yes, this is a non-probability sampling method because not all students have an equal chance of being selected (e.g., only students present on campus streets are considered). The sampling technique used here is convenience sampling.

Answer: It is a non-probability sampling method, specifically convenience sampling.

(v) Assume that university students from outside states are more likely to prefer hostel accommodation. What sampling method would you recommend? List the steps you would adopt to form the sample.

To ensure representation of students from outside states, a stratified random sampling method would be appropriate. This involves dividing the population into two strata: "students from outside states" and "students from the local area." Then, a random sample is selected from each stratum proportional to its size in the population.

Steps:

1. Identify the strata: Divide the students into two groups: those from outside states and those from the local area.
2. Determine the proportion: Calculate the percentage of students in each group.
3. Allocate the sample size: Divide the total sample size (100) proportionally between the two groups.
4. Randomly select students: Use simple random sampling within each stratum to select the required number of students.
5. Combine the samples: Merge the selected students from both strata to form the final sample.

Answer: Use stratified random sampling, following the steps listed above.

Do you want further clarification or additional details about any of the answers?

Related Questions:

1. What are the advantages of systematic sampling over random sampling?
2. How can bias in convenience sampling be minimized?
3. Why might stratified sampling be more accurate for heterogeneous populations?
4. What are the potential challenges of implementing stratified sampling in a university setting?
5. How does sample size affect the reliability of survey results?

Tip: Always consider the population characteristics when selecting a sampling method to avoid bias and ensure representativeness.