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!

Let's go through each part of the question and find the correct answers:

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 _____________

The answer is "less expensive". By using a sample instead of measuring every client, the manager can save resources and time.

The use of _____________ 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 answer is "statistical inference". Statistical inference allows the manager to make estimates about the population parameter (average weight-to-height ratio) based on the sample data.

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:

The answer is "c. The average weight-to-height ratio of all of the fitness center's clients." The manager is interested in estimating the average weight-to-height ratio of all clients in the fitness center.

The sample statistic is:

The answer is "a. The average weight-to-height ratio of the clients in the sample." The sample statistic is the calculated average weight-to-height ratio based on the sample data.

The sampling frame is:

The answer is "c. The set of the fitness center's clients from which the sample is drawn." The sampling frame is the list of all clients from which the sample was selected.

The population of interest is:

The answer is "a. All the fitness center's clients." The population of interest is the entire group of clients in the fitness center.

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

The answer is "A convenience sample" and "A volunteer sample." Both convenience samples and volunteer samples can introduce bias into the sample, as they may not represent the entire population accurately.

So, the correct answers are:
1. less expensive
2. statistical inference
3. c. The average weight-to-height ratio of all of the fitness center's clients
4. a. The average weight-to-height ratio of the clients in the sample
5. c. The set of the fitness center's clients from which the sample is drawn
6. a. All the fitness center's clients
7. A convenience sample and A volunteer sample