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Chapter 1: Problem 27

Marriage Rates The number of married people in the United States and the total number of adults in the United States (in millions) are provided in the accompanying table for several years. Find the percentage of people married in each of the given years, and describe the trend over time. (Source: 2009 World Almanac and Book of Facts) $$\begin{array}{|ccc|} \hline \text { Year } & \text { Married } & \text { Total } \\ \hline 1990 & 112.6 & 191.8 \\ \hline 1997 & 116.8 & 207.2 \\ \hline 2000 & 120.2 & 213.8 \\ \hline 2007 & 129.9 & 235.8 \\ \hline \end{array}$$

Short Answer

Expert verified
From 1990 to 2007, there was a downward trend in the percentage of adults married in the United States. Calculations indicate that the percentage decreased from approximately 58.69% in 1990 to approximately 55.12% in 2007.

Step by step solution

01

Calculate the percentage for each year

To calculate the percentage of people married in a given year, divide the number of married people by the total number of adults in that year and multiply it by 100. The formula is \(\ percentage = \frac{{\text{{Married}}}}{{\text{{Total}}}} \times 100\) This formula will be applied to the data of each year.
02

Percentage for the year 1990

Applying this formula for the year 1990, we get \( percentage = \frac{{112.6}}{{191.8}} \times 100 = 58.69% \). Hence approximately 58.69% of adults were married in the year 1990.
03

Percentage for the year 1997

Applying this formula for the year 1997, we get \( percentage = \frac{{116.8}}{{207.2}} \times 100 = 56.37% \). Hence, approximately 56.37% of adults were married in the year 1997.
04

Percentage for the year 2000

Applying this formula for the year 2000, we get \( percentage = \frac{{120.2}}{{213.8}} \times 100 = 56.22% \). Hence, approximately 56.22% of adults were married in the year 2000.
05

Percentage for the year 2007

Applying this formula for the year 2007, we get \( percentage = \frac{{129.9}}{{235.8}} \times 100 = 55.12% \). Hence, approximately 55.12% of adults were married in the year 2007.
06

Describe the trend

By comparing the calculated percentages, i.e., 58.69% (1990), 56.37% (1997), 56.22% (2000), and 55.12% (2007), it's observed that there is a downward trend in the rate of married adults in the US from 1990 to 2007.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistical Analysis
Statistical analysis involves collecting and analyzing data to identify patterns and trends. In the context of marriage rates, the raw data provided includes the number of married adults and the total number of adults for certain years. To analyze this data statistically, we first turn these raw numbers into meaningful percentages, as shown in the provided exercise steps.

By converting these figures into percentages, we transform the raw data into a form that allows for better comparison over time and across different population sizes. This is particularly important because the total number of adults changes every year, which could influence the number of married adults independently of the actual marriage trends.

Statistical analysis then extends to interpreting these percentages to understand broader social trends, such as the attitudes towards marriage or demographic changes. It allows us to transcend beyond the raw numbers to ask more nuanced questions, like 'Are fewer people choosing to get married, or are there other factors at play?'
Trend Analysis
Trend analysis is a technique used to predict future movements through historical data. Once we've calculated marriage percentages for different years, we proceed to compare them to observe whether there's an increasing or decreasing trend in marriage rates over time.

The step-by-step solution clearly delineates a downward trend in the marriage rates from 1990 to 2007. However, it's crucial to note that trend analysis mainly involves more than just observing the rise or fall of percentages; it includes looking for potential reasons behind these trends.

For instance, societal changes, such as shifting attitudes towards cohabitation or changing economic circumstances, can be influencing factors. Advanced trend analyses may also involve creating models to forecast future marriage rates based on current trends, which could be useful for sociologists, economists, and policymakers.
Percentage Calculation
Percentage calculation is a fundamental mathematical skill that allows us to express a number as a fraction of 100. It's widely used to compare and contrast data, as seen in the exercise with marriage rates.

The formula applied in the textbook solution, \( percentage = \frac{{\text{{Married}}}}{{\text{{Total}}}} \times 100 \), is essential for translating the raw marriage data into a more understandable and relatable form. This allows for a direct comparison of the prevalence of marriage among adults across different years.

Understanding how to calculate percentages is vital for interpreting data across various fields, not just in demographic studies. For example, knowing that the percentage of married individuals decreased from around 58.69% to 55.12% between 1990 and 2007 provides a clearer indication of marriage trends than the raw numbers alone.

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Most popular questions from this chapter

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The idea of sending delinquents to "Scared Straight" programs has appeared recently in several media programs (such as Dr. Phil) and on a program called Beyond Scared Straight. So it seems appropriate to look at a randomized experiment from the past. In 1983 , Roy Lewis reported on a study in California. Each male delinquent in the study (all were aged \(14-18\) ) was randomly assigned to either Scared Straight or no treatment. The males who were assigned to Scared Straight went to a prison, where they heard prisoners talk about their bad experiences there. Then the males in both the experimental and the control group were observed for 12 months to see whether they were rearrested. The table shows the results. (Source: Lewis, Scared straight - California style: Evaluation of the San Quentin Squires program. Criminal Justice and Behavior, vol. \(10: 209-226,1983\) ) $$\begin{array}{lcc} & \begin{array}{c} \text { Scared } \\ \text { Straight } \end{array} & \begin{array}{c} \text { No } \\ \text { Treatment } \end{array} \\ \hline \text { Rearrested } & 43 & 37 \\ \hline \begin{array}{l} \text { Not } \\ \text { rearrested } \end{array} & 10 & 18 \\ \hline \end{array}$$ a. Report the rearrest rate for the Scared Straight group and for the No Treatment group, and state which is higher. b. This experiment was done in the hope of showing that Scared Straight would cause a lower arrest rate. Did the study show that? Explain.
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