Question

Are boys more likely? We hear that newborn babies are more likely to be boys than girls. Is this true? A random sample of 25,468 firstborn children included 13,173 boys. Boys do make up more than half of the sample, but of course, we don't expect a perfect 50-50 split in a random sample.

(a) To what population can the results of this study be generalized: all children or all firstborn children? Justify your answer.

(b) Do these data give convincing evidence that boys are more common than girls in the population? Carry out a significance test to help answer this question.

Short answer

a. It can be generalized as the population of all firstborn children

b. These data give convincing evidence that boys are more common than girls in the population

Step-by-step solution

Introduction

Population size is the number of individuals in a population. Population density is the typical number of individuals per unit of region or volume. The example of spacing of individuals in a population might be impacted by the characteristics of a species or its environment.

Explanation Part (a)

Identify the population to which the aftereffects of the review can be generalized:

It is given that, an arbitrary example of $25468$firstborn children included $13173$ young men. Here, all the examples of children are firstborn children.

In this manner, the gathered example will address the population of firstborn children.

Henceforth, the outcomes can be generalized to all firstborn children.

Explanation Part (b)

Calculating the null and alternative hypotheses,

${\mathrm{H}}_0:\mathrm{p}=0.5$

${\mathrm{H}}_1:\mathrm{p}>0.5$

As per the null hypothesis, boys are not more common than girls and as per the alternative hypothesis boys are more common than girls.

The sample size is n = $25468$

Specified characteristics are x = $13173$

The sample proportion of boys

$\stackrel{-}{p}=\frac{x}{n}=\frac{13173}{25468}=0.517$

It is a right-tailed hypothesis.

The null hypothesis is rejected as the p-value is equal to a and is not rejected when the p-value is greater than a.

Hence these data give convincing evidence that boys are more common than girls in the population.