Worksheet 2: Life expectancy by sex: Teacher version

1. Who has a higher life expectancy, males or females? Approximately how many years of difference are there between the life expectancies of males and females (over the period from 1979 to 1999)?

   Females have a higher life expectancy by approximately six years. See graph below.

   
   Source: Statistics Canada. Table 102-0025 - Life expectancy, abridged life table, at birth and at age 65, by sex, Canada, provinces and territories (Comparable Indicators), annual (years), CANSIM (database), Using E-STAT (distributor).
   http://estat.statcan.ca/cgi-win/cnsmcgi.exe?Lang=E&ESTATFile=EStat\English\CII_1_E.htm&RootDir=ESTAT/
   (accessed: April 22, 2008)

2. By inspection, which line (life expectancy of males or females) appears to have a higher slope?

   The line of male life expectancy appears to have a higher slope.

3. Select two points on each line and estimate the slope using the equation . Show all calculations and be sure to note which points you chose for each line, as an ordered pair. Describe what each ordered pair means. Which line has a higher slope, according to your calculations? Was your guess by inspection correct?

   Note: It is important to select points that are far apart from each other, but close to the line of best fit in order to accurately estimate slope.

   Males: Points selected were (2, 72.1) and (19, 76). This means that for boys born two years after 1979 (1981), their life expectancy is 72.1 years whereas the life expectancy for boys born 19 years after 1979 (1998) is 76 years.

   
   =~ 0.2294

   Females: Points selected were (3, 79.4) and (18, 81.3). This means that for girls born three years after 1979 (1982), their life expectancy is 79.4 years whereas the life expectancy for girls born 18 years after 1979 (1997) is 81.3 years.

   
   =~0.1267

   The slope of the line for males is 0.2294, which is higher than the slope of the line for females (0.1267). My guess by inspection was correct.

4. For the graph of the life expectancy of males, write the equation of the line of best fit in two ways:
   • Slope-intercept form (y = mx + b)
   • Standard form (Ax + By + C = 0)

   y = 0.2299x + 71.668
   0.2299x – y + 71.668 = 0

5. For the graph of the life expectancy of females, write the equation of the line of best fit in two ways:
   • Slope-intercept form (y = mx + b)
   • Standard form (Ax + By + C = 0)

   y = 0.1357x + 79.052
   0.1357x – y + 79.052 = 0

6. Which line of best fit has a higher slope? What does this higher slope represent?

   The line of best fit for the life expectancy of males has a higher slope. This represents that for each year later than 1979 that a baby boy is born, the life expectancy will have a greater increase (0.2299 years for males versus 0.1357 years for females).

7. By inspection, approximately where do the lines intersect (as an ordered pair)? What does this represent?

   The lines appear to intersect at the point (80, 90). This means that for babies born 80 years after 1979 (in the year 2059), life expectancies of both males and females are predicted to be 90 years, according to the linear model.

8. Substitute the number of years since 1979 value (round to the nearest year) into your lines of best fit equations to confirm the life expectancy at the point of intersection.

   Years Since 1979 = 80

   Males:
   y = 0.2299x + 71.668
   y = 0.2299(80) + 71.668
   y = 18.392 + 71.668
   y = 90.06

   Females:
   y = 0.1357x + 79.052
   y = 0.1357(80) + 79.052
   y = 10.856 + 79.052
   y = 89.908

9. Staple a printout of your graph with the lines of best fit and point of intersection to this worksheet.

   
   Source: Statistics Canada. Table 102-0025 - Life expectancy, abridged life table, at birth and at age 65, by sex, Canada, provinces and territories (Comparable Indicators), annual (years), CANSIM (database), Using E-STAT (distributor).
   http://estat.statcan.ca/cgi-win/cnsmcgi.exe?Lang=E&ESTATFile=EStat\English\CII_1_E.htm&RootDir=ESTAT/
   (accessed: April 22, 2008)