Chapter 1, Problem 1CRE

Medication Usage In a survey of 3005 adults aged 57 through 85 years, it was found that 82% of them used at least one prescription medication (Journal of the American Medical Association). The margin of error is 1 percentage point.

1. a. Interpret the margin of error by identifying the range of values likely to contain the percentage of adults aged 57 through 85 years who use at least one prescription medication.
2. b. Identify the population.
3. c. Is this study an experiment or an observational study? Explain. Identify the variable of interest.
4. d. Is the reported value of 82% a population parameter or a sample statistic? Why?
5. e. If you learned that survey subjects responded to a magazine article asking readers to phone in their responses, would you consider the survey results to be valid? Why or why not?
6. f. Match each of the following with one of these sampling methods: simple random sampling, stratified sampling, cluster sampling, systematic sampling, or convenience sampling.
   1. i. Somehow obtain a list of all adults aged 57 through 85 years and select every 100th name on the list.
   2. ii. Use a computer to randomly generate telephone numbers and use only respondents between the ages of 57 through 85 years.
   3. iii. In each state, select about 60 subjects between the ages of 57 through 85 years.
   4. iv. Interview people you know who are between the ages of 57 through 85 years.
   5. v. Randomly select streets and interview all subjects living on those streets who are between the ages of 57 through 85 years.

To determine

Interpret the margin of error.

Explanation of Solution

In a survey of 3,005 adults with age 57 to 85 years, it is found that 82% of them use at least one prescription medication and the margin of error is 1 percentage point.

Margin of error:

The term margin of error is used to explain the range of values.

The range of values that contain the population parameter is,

 (Sample statistic – margin of error), (Sample statistic + margin of error).

The confidence interval for the population parameter is, $\left(82-1,82+1\right)=\left(81,83\right)$.

Thus, the confidence interval is $\left(81\%,83\%\right)$.

Thus, the confidence interval interprets that the percentage of adults with age 57 to 85 who used prescription medication at least once is between 81% to 83%.

To determine

Identify the population.

Answer to Problem 1CRE

The population contains all adults with age 57 to 85 years.

Explanation of Solution

Population:

The term population is the complete set of all observations in the study.

From the given experiment, the population contains all adults with age 57 to 85 years.

To determine

Identify whether the study is an experimental or an observational study.

Identify the variable of interest.

Explanation of Solution

Observational study:

In an observational study the researchers observe or measure the characteristic of the subjects, but do not try to modify or influence those characteristics.

Experimental study:

In an experimental study, the researchers apply a treatment to some or all subjects of the experiment and observe the treatment effects.

In the given survey, the researcher observes who are using at least once prescription medicine. Here, the researcher doses not modify the results.

Thus, the study is an observational experiment.

Variable of interest:

The term “variable of interest” in a statistical study is used to measure the items or quantities.

In the given experiment, the study is to check whether the adults are taking prescription medicine at least once.

Thus, the variability of interest is whether the adults are taking prescription medicine at least once.

To determine

Check whether the reported value ‘82%’ is a population parameter or a sample statistic.

Answer to Problem 1CRE

The 82% represents the sample statistic.

Explanation of Solution

Sample statistic:

The term sample statistic is the particular number that describes about the characteristic of the sample, which is found by summarizing the raw data.

Population parameter:

The term population parameter is the particular number that describes about the characteristic of the population.

From the given information, the 82% represents the sample statistic because the results are based on the sample of 3,005 adults with age 57 to 85 years. The results are not done based on the population.

Thus, the 82% represents the sample statistic.

To determine

Check whether the survey results are valid.

Explain the reason if they are not valid.

Answer to Problem 1CRE

The survey results are not valid.

Explanation of Solution

The survey subjects are collected by phone and the respondents have to call and mention the opinions leads to a self-selection bias because the respondents who are willing to give strong opinion only will respond.

Thus, the survey result is not valid.

To determine

Match the sampling methods.

Explanation of Solution

The different sampling methods are simple random sampling, stratified sampling, cluster sampling, systematic sampling or convenience sampling.

The five common sampling methods are as follows:

1. 1. Simple random sampling: Choose the sample of items with equal chance of priority.
2. 2. Systematic sampling: Selecting every 10^th or every 50^th member of the population.
3. 3. Convenience sampling: The sampling happens to be convenient to select.
4. 4. Cluster sampling: In cluster sample, first divide the population into groups, then select the clusters at random. Next, obtain the sample by choosing the all members within each of the selected clusters.
5. 5. Stratified sampling: These sampling is used when the data concerned with different sub groups within the population. In stratified sampling, first identify the groups, then draw a random sampling within each group.

Part (i): The given situation is to obtain a list of all adults with age 57 to 85 years and select every 100^th name on the list.

Selecting 100^th name in list represents the systematic sampling.

Part (ii): The given situation is to use the computer and generate telephone numbers randomly to find respondents between the ages of 57 through 85 years.

Selecting random numbers using computer represents the simple random sampling.

Part (iii): The given situation is that select 60 subjects between the ages of 57 through 85 years in each state.

Selection of 60 subjects from each state indicates that the first state is selected from that randomly subjects. It represents an example of the stratified sampling.

Part (iv): The given situation is that the known interview people is between the ages of 57 through 85 years.

The sample selection happened according to researcher’s convenience that represents the convenience sampling.

Part (v): The given situation is that select the streets randomly and takes interview of all subjects from those streets with age group 57 to 85 years.

Here, the streets are randomly selected and then all subjects of each street give responses. Thus, this represents the cluster sampling.