91Ó°ÊÓ

given,

One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25,0.50, and 0.25 for two girls, one girl and one boy, and two boys, respectively.

Null hypothesis:

$H_0:-$ Gender distribution in families with two children does not differ from the distribution predicted by the model described.

Another hypothesis:

$H_1:-$ The distribution of sex in families with two children differs from the predictive distribution of the model described.

MINITAB process:

Step 1: Select Number> Tables> Chi-Square-Goodness-of-Fit Test Test (One Variable)

Step 2: In the visual calculation, enter the "O" column.

Step 3: In the names of the categories, enter a column. "Gender".

Step 4: Under Test, select the "P" column for specific dimensions.

Step 5: Click OK.

According to the output, the value of the test statics is $185.080$and the p-value is 0.

Here, the value of p is smaller than the value level.

That is the value of $p(=0)<\mathrm{Î\pm }(=0.01)$.

Therefore, the null hypothesis was rejected at $1\%$.

Thus, the data provide sufficient evidence to conclude that gender distribution in families of two children differs from the predicted distribution of the model defined at the $1\%$ significance level.

There is very strong evidence against the null hypothesis because the value of p is almost zero. This means that the null hypothesis is rejected at the value of $1\%$. Therefore, it can be concluded that gender distribution in families of two children differs from the predicted propagation of the described model. That is, the model for child gender opportunities is that a boy or girl does not have an equal chance of being born.