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.

statistic

A statistic is a numerical characteristic of a sample that is used to estimate a population characteristic, such as the sample mean, which is used to estimate the population mean in statistics. For example, suppose the researcher wants to determine the average income of people in the United States aged 18 to 60. The parameter of the given sample is then the average income of those people selected in the sample who are between the ages of 18 and 60.

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

As a result, the statistic for the given data is the average length of time (in months) that AIDS patients in the given sample of 40 patients live after treatment.

Further, the average (mean) of the given sample can be calculated as:

$\overline{x}=\frac{\sum x}{n}$

Where,

$\sum x$= sum of the given average length of time of 40 AIDS patients

$n$=number of patients in the given sample

role="math" localid="1648028745227" $$\begin{gathered} \overline{x}=\frac{943}{40} \\ \overline{x}=23.575months \end{gathered}$$

The statistic for Researcher A is 23.575 months, which is the average (mean) length of time patients live in the given sample for Researcher A.