Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. Two researchers each follow a different set of 40 patients with AIDS from the start of treatment until their deaths. The following data (in months) are collected.

Researcher A:

3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

Researcher B:

3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Determine what the key terms refer to in the example for Researcher A.

sample

The sample is a portion of the population that is chosen and analyzed in order to derive conclusions about the entire population of interest in statistics.

Because studying the entire population is impractical and often very time-consuming and expensive, it is often essential to pick a sample from the population. For example, suppose the researcher wants to determine the average income of people in the United States aged 18 to 60. Knowing the income of everyone between the ages of 18 and 60 is a time-consuming and expensive task. As a result, in such a case, we simply analyze the group of persons aged 18 to 60 years and draw conclusions about the total population of people aged 18 to 60 years based on this sample. As a result, a sample is a group of persons picked from the general population.

For Researcher A, we have data in the given question about the average (mean) length of time in months that AIDS patients live once they begin treatment. The data is given below as:

Researcher A:

3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

Hence, the given information which consists of data of 40 AIDS patients is the sample in this case.

For the given information, the sample for Researcher A is 40 AIDS patients.