I have done parts of this question (they are capitalized)which I was hoping someone could double check, and there are other parts that I need help on.

1. The manager of a fitness center is interested in the average weight-to-height ratio of the center's clients. Since the manager does not have the resources to measure the height and weight of every client, she takes a sample and calculates the average weight to height ratio for the sample.
A major benefit of the fitness center manager using a sample rather than all the fitness center's clients is that it is _____________(less expensive, more expensive, MORE ACCURATE). The use of _____________(STATISTICAL INFERENCE, sampling error, graphical deception)allows the fitness center manager to estimate the population mean based on a sample that is quite small in comparison with the size of the population.
The fitness center manager's estimate of the population mean may be quite close to the actual mean, provided that its sample is representative of the population of interest.
The population parameter being estimated is:
a. The median weight-to-height ratio of all of the fitness center's clients.
b. The average weight-to-height ratio of the clients in the sample.
c. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF ALL OF THE FITNESS CENTER'S CLIENTS.

The sample statistic is:
a. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF THE CLIENTS IN THE SAMPLE.
b. The median weight-to-height ratio of all of the fitness center's clients.
c. The average weight-to-height ratio of all of the fitness center's clients

The sampling frame is:
a. The fitness center's clients in the sample
b. All the fitness center's clients
c. The set of the fitness center's clients from which the sample is drawn.
(I'm not sure about this one, is it C?)

The population of interest is:
a. All the fitness center's clients
b. The set of the fitness center's clients from which the sample is drawn.
c. The assumed population from which the sample of the fitness center's clients is drawn.
(Again, not sure. I think it might be C)

It may not be the case that the fitness center manager's sampling frame is the same as its population of interest. This is a major problem for the fitness center manager because it can lead to poor parameter estimates. This problem may likely occur if the fitness center manager's sample is which of the following? Check all that apply
A probability sample
An unbiased sample
A CONVENIENCE SAMPLE
A VOLUNTEER SAMPLE

Thank you to anyone who helps me on this!

1. The major benefit of the fitness center manager using a sample rather than all the fitness center's clients is that it is MORE ACCURATE. The use of STATISTICAL INFERENCE allows the fitness center manager to estimate the population mean based on a sample that is quite small in comparison with the size of the population.

The population parameter being estimated is: c. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF ALL OF THE FITNESS CENTER'S CLIENTS.

The sample statistic is: a. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF THE CLIENTS IN THE SAMPLE.

The sampling frame is: c. The set of the fitness center's clients from which the sample is drawn.

The population of interest is: b. The set of the fitness center's clients from which the sample is drawn.

The fitness center manager's sampling frame may not be the same as its population of interest. This is a major problem for the fitness center manager because it can lead to poor parameter estimates. This problem may likely occur if the fitness center manager's sample is a CONVENIENCE SAMPLE and/or a VOLUNTEER SAMPLE.

To answer these questions, let's break them down one by one:

1. The benefit of the fitness center manager using a sample rather than all the clients is that it is _____________ (less expensive, more expensive, MORE ACCURATE).
The correct answer is "more accurate." Using a sample allows the manager to gather information about a subset of the clients and make inferences about the entire population. By using statistical techniques, the manager can estimate the population parameters with a high degree of accuracy without having to measure every client.

2. The use of _____________ (STATISTICAL INFERENCE, sampling error, graphical deception) allows the fitness center manager to estimate the population mean based on a sample that is quite small in comparison with the size of the population.
The correct answer is "statistical inference." Statistical inference refers to the process of drawing conclusions about a population based on a sample. By using statistical techniques, the fitness center manager can make accurate estimates of the population mean even with a small sample size.

3. The population parameter being estimated is:
The correct answer is: "c. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF ALL OF THE FITNESS CENTER'S CLIENTS." The population parameter refers to the characteristic of the entire population that is being estimated, in this case, the average weight-to-height ratio of all clients.

4. The sample statistic is:
The correct answer is "a. THE AVERAGE WEIGHT-TO-HEIGHT RATIO OF THE CLIENTS IN THE SAMPLE." The sample statistic refers to the characteristic of the sample that is being measured, in this case, the average weight-to-height ratio of the clients in the sample.

5. The sampling frame is:
The correct answer is "c. The set of the fitness center's clients from which the sample is drawn." The sampling frame refers to the list or set of all elements from which the sample is selected, in this case, the set of clients from which the sample is drawn.

6. The population of interest is:
The correct answer is "c. The assumed population from which the sample of the fitness center's clients is drawn." The population of interest refers to the larger group or population from which the sample is drawn, in this case, the assumed population from which the sample of the fitness center's clients is drawn.

7. The problem that may occur for the fitness center manager, leading to poor parameter estimates, is when the sample is which of the following? Check all that apply
The correct answers are: "A CONVENIENCE SAMPLE" and "A VOLUNTEER SAMPLE." Convenience samples and volunteer samples are non-probability sampling methods that may introduce biases into the sample, making it unrepresentative of the population. This can lead to poor parameter estimates.

I hope this helps! Let me know if you have any further questions.