2.102 Remote deposit capture

The Federal Reserve has called remote deposit capture (RDC) “the most important development the [U.S.] banking industry has seen in years.” This service allows users to scan checks and to transmit the scanned images to a bank for posting.¹⁶ In its annual survey of community banks, the American Bankers Association asked banks whether or not they offered this service.¹⁷ Here are the results classified by the asset size (in millions of dollars) of the bank:

Summarize the results of this survey question numerically and graphically. Write a short paragraph explaining the relationship between the size of a bank, measured by assets, and whether or not RDC is offered.

2.103 How does RDC vary across the country?

The survey described in the previous exercise also classified community banks by region. Here is the 6 × 2 table of counts:¹⁸

Summarize the results of this survey question numerically and graphically. Write a short paragraph explaining the relationship between the location of a bank, measured by region, and whether or not remote deposit capture is offered.

2.104 Exercise and adequate sleep

A survey of 656 boys and girls, ages 13 to 18, asked about adequate sleep and other health-related behaviors. The recommended amount of sleep is six to eight hours per night.¹⁹ In the survey, 54% of the respondents reported that they got less than this amount of sleep on school nights. The researchers also developed an exercise scale that was used to classify the students as above or below the median in how much they exercised. Here is the 2 × 2 table of counts with students classified as getting or not getting adequate sleep and by the exercise variable:

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2.105 Adequate sleep and exercise

Refer to the previous exercise.

2.106 Full-time and part-time college students

The Census Bureau provides estimates of numbers of people in the United States classified in various ways.²⁰ Let’s look at college students. The following table gives us data to examine the relation between age and full-time or part-time status. The numbers in the table are expressed as thousands of U.S. college students.

2.107 Condition on age

Refer to the previous exercise.

2.108 Lying to a teacher

One of the questions in a survey of high school students asked about lying to teachers.²¹ The accompanying table gives the numbers of students who said that they lied to a teacher about something significant at least once during the past year, classified by gender.

2.109 Trust and honesty in the workplace

The students surveyed in the study described in the previous exercise were also asked whether they thought trust and honesty were essential in business and the workplace. Here are the counts classified by gender:

Answer the questions given in the previous exercise for this survey question.

2.110 Class size and course level

College courses taught at lower levels often have larger class sizes. The following table gives the number of classes classified by course level and class size.²² For example, there were 202 first-year level courses with between one and nine students.

2.111 Hiring practices

A company has been accused of age discrimination in hiring for operator positions. Lawyers for both sides look at data on applicants for the past three years. They compare hiring rates for applicants younger than 40 years and those 40 years or older.

2.112 Nonresponse in a survey of companies

A business school conducted a survey of companies in its state. It mailed a questionnaire to 200 small companies, 200 medium-sized companies, and 200 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the data on response to this survey:

2.113 Demographics and new products

Companies planning to introduce a new product to the market must define the “target” for the product. Who do we hope to attract with our new product? Age and gender are two of the most important demographic variables. The following two-way table describes the age and marital status of American women.²³ The table entries are in thousands of women.

2.114 Demographics, continued

2.115 Demographics and new products—men

Refer to Exercises 2.113 and 2.114. Here are the corresponding counts for men:

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Answer the questions from Exercises 2.113 and 2.114 for these counts.

2.116 Discrimination?

Wabash Tech has two professional schools, business and law. Here are two-way tables of applicants to both schools, categorized by gender and admission decision. (Although these data are made up, similar situations occur in reality.)

2.117 Obesity and health

Recent studies have shown that earlier reports underestimated the health risks associated with being overweight. The error was due to lurking variables. In particular, smoking tends both to reduce weight and to lead to earlier death. Illustrate Simpson’s paradox by a simplified version of this situation. That is, make up tables of overweight (yes or no) by early death (yes or no) by smoker (yes or no) such that

2.118 Find the table

Here are the row and column totals for a two-way table with two rows and two columns:

Find two different sets of counts a, b, c, and d for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.