Question

A fitness center is interested in the mean amount of time a client exercises in the center each week. Define the following in terms of the study. Give examples where appropriate.

Part (a)
The population
The population is the total amount of time a client exercises in one week.
The population is all of the clients that use the fitness center for a given week.
The population is all of the clients of the fitness center.
The population is all of the clients sampled by the fitness center.
Part (b)
The sample
The sample would be the days of the week in which the most clients use the fitness center.
The sample would be the total amount of time a client exercises in one week.
The sample would be all of the clients of the fitness center.
The sample would be all of the clients that use the fitness center for a given week.
Part (c)
The parameter
The parameter is the average amount of time that a sample of clients exercises in one week.
The parameter is the average number of visits per day for one week.
The parameter is the average amount of time that all clients exercise in one week.
The parameter is the number of clients who visit the fitness center in one week.
Part (d)
The statistic
The statistic is the average amount of time that all clients exercise in one week.
The statistic is the average amount of time that a sample of clients exercises in one week.
The statistic is the number of clients who visit the fitness center in one week.
The statistic is the total amount of time that all clients exercise in one week.
Part (e)
The variable
The variable is the amount of time that a client exercises in one week.
The variable is the number of clients that visit the fitness center each day.
The variable is the average number of visits per week for all clients.
The variable is the number of days per week that a client visits the fitness center.
Part (f)
The data
Examples: 5 weeks, 1 week, 2 weeks
Examples: 5 days, 2 days, 3 days
Examples: 5 hours, 3 hours 30 minutes, 2 hours 45 minutes
Examples: 58 clients, 25 clients, 90 clients

Answer 1

In a study by a fitness center to find the mean exercise time per week, the population is all clients, the sample is a portion of these clients, the parameter is the true average time for all clients, the statistic is the average time for the sample, the variable is the weekly exercise time per client, and the data are the actual exercise times recorded.

Step-by-step explanation:

When a fitness center is interested in determining the mean amount of time a client exercises each week, various statistical terms are used to describe different aspects of this study:

• Population: Refers to all the clients of the fitness center. An example would be every client who has a membership.
• Sample: A smaller group selected from the population which will be used to gather data. An example could be 150 clients chosen at random from the total membership list.
• Parameter: This is the actual average amount of time that all the clients in the population exercise in one week. It is a characteristic we aim to estimate.
• Statistic: The statistic refers to the average amount of time that the sample of clients exercises in one week, which is used to estimate the parameter.
• Variable: This is the specific quantity we are interested in measuring, in this case, the amount of time each client exercises in the fitness center over one week.
• Data: These are the actual measurements or observations collected from the sample. Examples include the number of minutes each client in the sample exercises, like 210 minutes, 150 minutes, and 180 minutes.