A researcher studying a hidden population cannot construct a full list of members. Which sampling approach below is most appropriate because it does not rely on a full frame?

A public health agency has a roster of all $\mathrm{250,000}$ households in a city and plans to select a systematic sample of $200$ households to inspect. Determine the sampling interval, $k$.

To study the effects of different diets on energy levels, $150$ volunteers agreed to participate in an experiment. They will be assigned to one of four diet groups, including a control group. Describe how you could design this experiment using a randomized block design.

A university administration wants to find out the most preferred study spot among $12,000$ students on campus. Should they conduct a census or use sampling? If sampling is preferred, what sampling technique should they use? Explain your reasoning.

A health researcher wants to study exercise habits among employees at a large company. Employees are first grouped by department, such as HR, IT, marketing, and sales, and then a random sample is selected from each department. What type of sampling is this?

To gather opinions on campus dining, a student stands outside the cafeteria at lunchtime and interviews $40$ students who are leaving. What sampling technique is used, and what are the potential sources of bias?

A university wants to assess student satisfaction with campus dining. They survey every $10$^th student entering the main cafeteria during lunch hours over a week. What sampling method is being used, and what biases might be present?

A research team is evaluating the effectiveness of a new breathing technique for reducing anxiety in young adults. A total of $36$ participants aged $18\text{–}19$, all diagnosed with mild anxiety, volunteer for the study. They are randomly assigned to practice either the breathing technique or a control activity (sitting quietly) each day for $4$ weeks. Anxiety levels are measured using two standard psychological scales at the beginning and end of the study. Identify one potential problem in this experimental design and suggest a way to improve it.

A fitness researcher wants to compare two exercise programs. She recruits $160$ volunteers and first separates them into groups based on whether they exercise regularly or not. Within each group, volunteers are randomly assigned to one of the two exercise programs. What type of experimental design is this?

Researchers partition the population into naturally occurring groups and then randomly select a few groups, measuring every member in those selected groups. What type of sampling method is being described?