414 Age at first marriage Part I The National Survey of Fami

4.14 Age at first marriage, Part I. The National Survey of Family Growth conducted by the Centers for Disease Control gathers information on family life, marriage and divorce, pregnancy, infertility, use of contraception, and men\'s and women\'s health. One of the variables collected on this survey is the age at first marriage. The histogram below shows the distribution of ages at first marriage of 5,534 randomly sampled women between 2006 and 2010. The average age at rst marriage among these women is 23.44 with a standard deviation of 4.72.44 Age at first marriage 10 15 20 25 30 35 40 45 0 200 400 600 800 1000 Estimate the average age at rst marriage of women using a 95% condence interval, and interpret this interval in context. Discuss any relevant assumptions.

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=23.44
Standard deviation( sd )=4.72
Sample Size(n)=5534
Confidence Interval = [ 23.44 ± Z a/2 ( 4.72/ Sqrt ( 5534) ) ]
= [ 23.44 - 1.96 * (0.063) , 23.44 + 1.96 * (0.063) ]
= [ 23.316,23.564 ]