The First Large-Scale Study of the Human Sex Ratio Involved

question 13

Essay

The first large-scale study of the human sex ratio involved over 6,000 families each having 12 children. (This was done in 19th Century Germany--large families were more common then and there.) 52% of the children they observed were boys. Suppose that 21st Century researchers wish to replicate this observational study. In order to see if this proportion of boys might have changed in the intervening years, suppose the researchers track down 50 families with 12 children. From these 600 children, a random sample of 50 children is taken. 30 of the 50 children were boys ( = 0.6.)a)Show that it is reasonable to approximate the sampling distribution of using a normal distribution.
b)If the modern true population proportion of newborn boys is p = 0.52, what is the probability of observing a sample proportion of at least = 0.6?

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Definitions:

Yield Interest

The interest generated from an investment, usually expressed as an annual percentage of the investment's cost.

Present Value

Today's value of a future money sum or series of cash flows, estimated using an agreed upon return rate.

Actuarial Information

Data and analysis related to the calculation of insurance risks and premiums, often involving life expectancy, health risks, and financial implications.

Bond Issue

The process by which a company or governmental entity raises funds by selling bonds to investors, which are debt securities obligating the issuer to pay interest and repay principal at a later date.