Does the rare male advantage result from faulty experimental design?

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...

In most mammalian species, females have two X sex chromosomes and males have an X and Y. As a result, mutations on the X chromosome in females may be masked by the presence of a normal allele on the second X. In contrast, a mutation on the X chromosome in males more often causes observable biological defects, as there is no normal X to compensate. Trait variations arising from mutations on the X chromosome are called “X-linked”.

The Y chromosome is a sex chromosome found in several vertebrates and mammals, including humans. In addition to 22 pairs of autosomes, the human males have one X chromosome and one Y chromosome. In these organisms, the presence or absence of the Y chromosome determines the development of male traits.
Evolution
Around 300 million years ago, the two sex chromosomes diverged from two identical autosomal chromosomes. Over time, the Y chromosome has lost most of its genes, shrinking in size. Today,...

In most organisms, sex is determined by the ratio of X and Y chromosomes. However, in some organisms, such as Drosophila and C.elegans, sex is determined by the ratio of the number of X chromosomes to the number of sets of autosomes. The Y chromosome in Drosophila is active but does not determine sex. It contains genes responsible for the production of sperms in adult flies.  
Normal male Drosophila has a ratio of one X chromosome to two sets of autosomes. In contrast, normal female Drosophila...

In animals, gender is determined by the number and type of sex chromosome. For example, human females have two X chromosomes, and males have one X and one Y chromosome, whereas C.elegans with one X chromosome is a male, and the one with two X chromosomes is a hermaphrodite.
In addition to sexual development, the X chromosome has genes involved in autosomal functions such as brain development and the immune system. Therefore, males and females with  distinct numbers of X chromosomes will have...

Mate choice—the decision about whom to mate with—is a type of natural selection, since animals must reproduce to pass down their genes. Mate choice is also called intersexual selection because the behavior occurs between the sexes.