A Bloomberg Businessweek North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indic

Result:
a. The population of interest is the group of Bloomberg Businessweek subscribers in North America.
b. The variable 'annual income' is a quantitative variable.
c. The variable 'ownership of an American Express card' is a categorical variable.
Solution:
a. To determine the population of interest in this study, we need to consider who the study is focused on. In this case, the population of interest is the group of Bloomberg Businessweek subscribers in North America. The sample size of 2861 subscribers represents a subset of this population.
b. The variable 'annual income' is a quantitative variable. A quantitative variable is one that can be measured numerically and can take on a wide range of values. In this study, the respondents were asked to indicate their annual income, which typically involves providing a numerical value (e.g., 75,000). Quantitative variables can be further categorized as discrete or continuous, depending on whether the values can take on only specific points or any value within a given range. However, without additional information about the options or response scale provided for income, we cannot determine whether it is discrete or continuous.
c. The variable 'ownership of an American Express card' is a categorical variable. A categorical variable is one that represents qualitative characteristics or attributes and is typically expressed in non-numeric terms. In this case, the respondents were asked whether they have an American Express credit card, which can be answered with 'yes' or 'no.' Categorical variables can be further classified as nominal or ordinal, depending on the level of measurement. Nominal variables have categories with no inherent order, while ordinal variables have categories that can be ordered or ranked. Without additional information, we cannot determine whether ownership of an American Express card is nominal or ordinal in this study.

Explanation:
a. The population of interest in this study can be represented as $P$.
b. Annual income is a quantitative variable as it represents a numerical value.
c. Ownership of an American Express card is a categorical variable as it represents a membership category (either having the card or not having it).

Step 1:
a. To determine the population of interest in this study, we refer to the information given, which states that the sample consists of '2861 Bloomberg Businessweek subscribers in North America.' Therefore, the population of interest in this study is the total number of Bloomberg Businessweek subscribers in North America.
Step 2:
b. To determine whether annual income is a categorical or quantitative variable, we can analyze the given information. The statement indicates that '59% of the respondents indicated an annual income of 75,000 dollars or more.' Since income is measured in specific dollar amounts and can take on a range of numerical values, it is considered a quantitative variable.
Step 3:
c. Similarly, to determine whether ownership of an American Express card is a categorical or quantitative variable, we analyze the provided data. The statement mentions that '50% reported having an American Express credit card.' As ownership of an American Express card can be classified as a yes/no or binary choice, it is considered a categorical variable.
Step 4:
Therefore, the answers are:
a. The population of interest in this study is the total number of Bloomberg Businessweek subscribers in North America.
b. Annual income is a quantitative variable.
c. Ownership of an American Express card is a categorical variable.