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Local Human Longevity: Female vs. Male

Introduction

It is often heard that female and males do not share the same life expectancy. According to the National Vital Statistics Reports, the average life expectancy for a female is 80.2 years and for a male 75.1 years, as of 2006. To test how these number correlate with the local distribution, I have assembled data consisting of 25 female’s age at death and 25 male’s age at death from a local cemetery located in Hammond, Indiana. All deceased passed within the years 2000-2010.

Data

MALES Death within 2000-2010
Birth year	Death year	Age at death
1920	2006	86
1946	2007	61
1957	2006	48
1917	2006	89
1929	2001	72
1911	2010	99
1913	2004	91
1916	2005	89
1923	2001	78
1913	2004	89
1922	2001	79
1924	2009	85
1909	2004	95
1924	2004	80
1949	2004	55
1939	2003	64
1959	2006	47
1930	2010	80
1918	2005	87
1924	2009	85
1919	2002	83
1941	2003	62
1918	2007	89
1922	2001	79
1913	2007	94

Table 1

FEMALES 2000-2010 death year
Birth year	Death year	Age at death
1913	2008	95
1917	2010	93
1911	2004	93
1934	2007	73
1914	2001	87
1910	2001	91
1906	2003	97
1918	2000	82
1918	2011	93
1922	2001	79
1922	2003	81
1913	2003	90
1917	2008	91
1935	2003	68
1910	2001	91
1949	2004	55
1916	2006	90
1911	2010	99
1919	2005	86
1921	2002	81
1919	2010	91
1913	2006	93
1919	2002	83
1913	2002	89
1913	2002	89

Table 2

Histograms below dimply the frequency distribution of the age at the time of death for both male and female in Hammond, IN.

Numerical Summary are provided in the table 3 and table 4

Females Summary
Minimum	55
1st Quartile	70
Median	90
3rd Quartile	93
Max	99
Mean	86.4

Males Summary
Minimum	47
1st Quartile	70
Median	84
3rd Quartile	89
Max	99
Mean	78.625

Table 3 Table 4

We would like to test whether there is a difference in the survival time based on the gender. We will test the following hypothesis. Let denote the mean life expectancy for male and female respectively. We will test the following hypothesis.

Below is the computer output from the data analysis

> t.test(Female, Male)

Welch Two Sample t-test

data: Female and Male

t = 2.2148, df = 42.008, p-value = 0.03225

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

0.6891875 14.8308125

sample estimates:

mean of x mean of y

86.40 78.64

Decision: Since p-value=0.03225 is less than standard value 0.05 level of significance we reject the null hypothesis and conclude that there is a significance difference in the life expectancy of male and female. Also note that 95% confidence interval for the difference in the life expectancy is (0.69, 14.83).

Discussion

With the relatively small sample size it is apparent the life expectancies do differ. The female longevity average was 86.4 and the male longevity average was 78.64, giving the difference of 7.76 years.

Additionally, with hypothesis testing, it was significant that females do not have the same life expectancy as males (p=0.03225).

References Arias, E. (2010). United States Life Tables, 2006. National Vital Statistics Reports, 58(21), 1-40.

Male Survivorship 2000-2010

lx 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1 1 1 1 1 1 1 1 1 1 0.96000000000000063 0.96000000000000063 0.92 0.76000000000000123 0.76000000000000123 0.72000000000000064 0.6800000000000006 0.44000000000000006 0.2 4.0000000000000022E-2 0

Age (years)

Proportion surviving (lx)

Female Survivorship 2000-2010

lx 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1 1 1 1 1 1 1 1 1 1 1 1 0.96000000000000063 0.96000000000000063 0.92 0.88 0.84000000000000064 0.68 0.52 0.12000000000000002 0

Age (years)

Proportion surviving (lx)

Female

Male

Female

Male

Histogram of Female

Age

Frequency

5060708090100

Histogram of Male

Age

Frequency

405060708090100

FemaleMale

100

Boxplot of the life expectancy

Female

Male

and