1.4.2: Exercise N.4

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(1) The average annual snowfall for Cincinnati, OH is 23.3 inches. Buffalo, NY, receives an average of 95.4 inches. Fill in the blanks:

(a) Buffalo receives, on average, ______ % more snow than Cincinnati. Round to the nearest percent.

(b) Cincinnati receives, on average, ______ % less snow than Buffalo. Round to the nearest percent.

(2) The U.S. Census Bureau tracks changes in total population as well as populations within age groups. Between 2010 and 2020, the population 65 years and over increased at a rate of 38.6% . This increase is significantly greater than the total growth rate for the U.S. population of 7.4% during the same period.¹⁴

(a) Explain carefully what 38.6 percent refers to in the above statement.

(b) Explain carefully what 7.4 percent refers to in the above statement.

(c) Come up with a specific example (with numbers!) that illustrates the statement from the census. Your numbers do not have to agree with the actual U.S. population, they just need to describe a situation that agrees with the U.S. Census statement at the start of this problem.

(3) The U.S. Census Bureau also reported that in 1920 approximately 4.7% of the U.S. population was made up of individuals who were 65 years or older, while in 2020 this same age group made up about 16.8% of the population.

(a) Write a complete sentence that describes the absolute change in the number of people 65 years or older.

(b) Write a complete sentence that describes the relative change in the number of people 65 years or older.

(4) The U.S. population increased by 22.7 million people from 2010 to 2020. This was a 7.4% increase.¹⁵ According to these figures, what was the U.S. population in the years 2010 and 2020? Round to the nearest million.

(5) The Centers for Disease Control and Prevention (CDC) frequently report statistics related to motor vehicle safety. The proportion of drivers reportedly distracted at the time of a fatal crash has increased from 7 percent in 2005 to 13 percent in 2020.”¹⁶

(a) What does the 7 percent refer to in the above statement? What does the 13 percent refer to?

(b) If someone claimed that this represents a 6% increase in the proportion of drivers that were distracted at the time of a fatal crash, would that be true or false? Explain.

(6) In 2009, the federal minimum wage in the United States increased from $6.55 per hour (in 2008) to $7.25 per hour (in 2009). By what percentage did the minimum wage increase? Round to the nearest tenth of a percent.

(7) A Pew Research Center survey found that in 2004, 31% of adults in the U.S. supported gay marriage, and in 2021, 61% supported gay marriage.¹⁷ Which of the three statements below are correct? Select all that apply. All results are rounded to the nearest percent or percentage point.

(i) Between 2004 and 2021, the number of people who support gay marriage increased by 97%.

(ii) Between 2004 and 2021, the number of people who support gay marriage increased by 30%.

(iii) Between 2004 and 2021, the number of people who support gay marriage increased by 30 percentage points.

(8) According to the CDC, in 2002, 4.3% of youths in the United States aged 12–13 years used alcohol. In 2019, this percentage dropped to 1.7%.¹⁸

(a) Write a complete sentence that describes the decline in illicit drug use among youth aged 12–13 years by measuring absolute change.

(b) Write a complete sentence that describes the decline in illicit drug use among youth aged 12–13 years by measuring relative change.

(9) The following table is an excerpt of some statistics from the CDC concerning the smoking behavior of mothers in the United States in 2016:¹⁹

Education of Mother	Percent of Mothers 25 Years of Age and over who Smoked Cigarettes
Less than 12 years	11.7
High school diploma or GED	12.2
Some college or associate’s degree	7.9
Bachelor’s degree	1.0
Master’s degree or higher	0.4

(a) Describe carefully the numerator and denominator that make up the 11.7% in the above table.

(b) Notice that in the first two rows, the percent changes from 11.7% to 12.2%. Find the absolute and relative change in this data. Round to nearest tenth of a percentage point and tenth of a percent.

(c) Using complete sentences, compare the two percentages discussed in Question 9(b). Your comparison should include statements about absolute change, relative change, and the relationship between the educational backgrounds of the individuals involved.

____________________________________

¹⁴ https://www.census.gov/library/stories/2023/05/2020-census-united-states-older-population-grew.html

¹⁵ https://www.census.gov/library/stories/2021/08/more-than-half-of-united-states-counties-were-smaller-in-2020-than-in-2010.html.

¹⁶ https://www.forbes.com/sites/larrymagid/2012/06/10/cdc-study-too-many-teens-text-while-driving/#4397519b7302 and https://www.cdc.gov/niosh/motorvehicle/topics/distracteddriving/default.html

¹⁷ https://www.pewresearch.org/short-reads/2022/11/15/about-six-in-ten-americans-say-legalization-of-same-sex-marriage-is-good-for-society

¹⁸ https://www.cdc.gov/nchs/data/hus/2020-2021/SubUse.pdf

¹⁹ https://www.cdc.gov/nchs/data/databriefs/db305.pdf