Question

Age at first marriage, part 1. The National Survey of Family Growth conducted by the Centers for Disease Control gathers information on family life, marriage and divorce, pregnancy, infertility, us 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 first marriage among these women is 23.44 with a standard deviation of 4.72.

Estimate the average age at first marriage of women using 95% confidence interval, and interpret this interval in context. Discuss and relevant assumptions.

Answer 1

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AS FOR GIVEN DATA...

S0LUTION ::-

A 95% CI means a Z value of 1.96.

Average age is 23.44 and std dev is 4.72.

hence CI is Mu +/- Z*Sigma/Sqrt(n)

= 23.44 + 1.96*4.72/sqrt(5534) to 23.44 - 1.96*4.72/sqrt(5534)

= 23.31 to 23.54 . These are the CI bounds.

Further interpretation

The standard deviation of sample is quiet less, as the sample size is very high. Higher the sample size the lesser is going to be the CI limits, as can be seen from the lower and upper bounds of the values.

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