Question

In 2015, the Nellie Mae organization conducted an extensive study of how college students used credit cards. Two of their goals were to estimate the percentage of college students that have a credit card and the average credit card balance. To do this they randomly selected data for 600 undergraduate students aged 18-24 attending four-year public and private colleges across the United States who had applied for a loan with Nellie Mae during the summer and fall of 2001.

a) Identify the observational units.

b) Identify the population and sample of interest here.

c) Identify a categorical variable of interest and a quantitative variable of interest. Nellie Mae found that 83% of these undergraduate students carried at least one credit card, and that the average balance was $2327.

d) Are these numbers statistics or parameters? Explain how you can tell.

e) Would you expect the median credit card balance to be larger than the mean, smaller than the mean, or about the same as the mean? Explain your reasoning.

Answer 1

A) a unit of observation is the unit described by the data that one analyzes. Here unit of observation is 600 college college students.

B) the population of interest is College students. The students are randomly selected to make inference about population. This population of interest represents the entire population in a statistical analysis.

The sample of interest is undergraduate college students aged 18-24 with credit Card. This is because the data will collected for this group and analysis will be made.

C) categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Quantitative variable are numerical variables: counts, percents, or numbers.

The categorical variable of interest is whether the student is having credit Card or not. This is because the answer to this is yes or no which is limited, fixed and qualitative.

The quantitative variable of interest is average credit card balance. This is because balance is numerical in nature and can be measured.

D) statistic is any number computed from sample data. Hence the given both the numbers are statistic.

E) we expect the sample data to be positively skewed i.e. large number of students will have lower balance and fewer number of students will have higher balance. For the positively skewed data median is lower than mean. Hence, we expect median to be less than $2327.