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Hmm. It's also worth considering the possibility that the sex of the child could affect the appetite of the mother.
That's a much better hypothesis, in my opinion.
Exactly. Correlation does not imply causation.

Whenever I hear about various things that supposedly make children smarter, like listening to Mozart as a baby, playing a musical instrument, or having a fish as a pet, I can't help but think in almost every case it has much more to do with the type of environment the child is raised in.

There was a good "Bullshit!" episode (Penn and Teller) about exactly that.

Yes and it might be that smarter parents will play Mozart for a baby, and read to them, and have them learn a musical instrument. I'm not saying none of these things can possibly affect anything on their own, but just that you have to take extreme care with these kinds of statistics before making conclusions. And that kind of care seems to be lacking in articles like the parent.
Two more theories consistent with the data are:

(1) neither affects either; (2) eating more calories creates more girls

No. 2 might seem weird but consider the fact that using the brake pedal creates fewer car accidents despite the strong positive correlation of braking with accidents.

Without testing between competing explanations, there is no science, only depleted research funds :-(

This study refers only to the moment of conception.
Of course, it might also be the case that between the 9 day trip from the Fallopian tubes to the uterus the mother's diet affects the fertility conditions of her uterus differently for XY and XX offspring (for example, making it 50% likely for an XX to implant itself but only 45% for an XY to implant).
Interesting but I now officially remain skeptical of all studies where they don't introduce the studied mechanism in a random fashion (ie take people and make them eat a lot of calories or not) and they haven't identified a mechanism. At best this kind of research simply gives some impetus for further inquiry.
Isn't it the father's sperm that carries the X or the Y x-some that determines the sex of the baby? How could the mother's state determine which sperm is accepted to be "the one"?
It's not that simple. It is well-known from other research studies, particularly the ones which document the effect of social status on gender ratio, that the woman does have an ability to influence the gender ratio of her children. The most likely mechanism by which she does this is altering the porosity of her cervical channels, which could change the ratio of male to female sperm, but as far as I know no one has observed this directly.
The article poses a possible explanation at the end. The development of a fertilized embryo depends completely on the mother. Perhaps certain conditions reduce the viability of male embryos or increase the viability of female embryos. That seems like a simpler explanation than some sort of sperm selection.
Maybe they shouldn't have tracked sex of a child as compared to the weather on the day of conception or delivery of the child. To work out if kids conceived on a rainy day where more likely to be boys or girls.

I have a confession to make. I don't read any newspapers or listen to any tv/radio news. As they have a tendency of giving credit to anything. They'll put results taken from one study and publish it as if they are really statistically significant. One of the worst things is people who don't understand science commenting on it.

One study of 740 women among maybe a million times that number every year, is meaningless. They could have as easily tracked the weather and found out that 55% of the kinds conceived on rainy days were boys.