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A hypothesis is a reasonable assumption for a behaviour (plural hypotheses). The scholarly approach involves that an assumption be validated before it can be deemed a factual prediction. Technical speculations are mainly influenced by past results that cannot be fully addressed by established scientific findings.

Let's start by deciding on the null and alternate hypotheses:

The null hypothesis indicates that the proportion of Chinese girls born is $46.7\%$, while the alternative hypothesis states that the proportion of Chinese girls born is not $46.7$percent.

$$\begin{gathered} H_0:p=46.7\% \\ {H}_a:p鈮�46.7\% \end{gathered}$$

The random variable here is the proportion of Chinese girls born. As a result, for this test, we'll utilise the normal distribution.

$N\left(0.467,\sqrt{\frac{(0.467)(0.533)}{150}}\right)$

Then the $z-$test is

$z=\frac{p^{\text{'}}-p}{\sqrt{\frac{p(1-p)}{n}}}$

Here, $p\text{'}$is the observed proportion, and we calculate $p\text{'}$using the following method, where n is the sample size of $50$people:

$p\text{'}=\frac{x}{n}$

$$\begin{gathered} =\frac{60}{150} \\ =0.4 \end{gathered}$$

Substitute the $p\text{'}$value

$z=\frac{p^{\text{'}}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$$\begin{gathered} =\frac{-0.067}{0.04074} \\ =-1.645 \end{gathered}$$

Let's use the following formula to determine the p-value for a two-tailed test:

$$\begin{gathered} P=2脳P\left(z>/z_{\text{stat}}/\right) \\ P=2脳P\left(z>1.645\right) \\ P=2脳[1-P\left(z>1.645\right)] \end{gathered}$$

$$\begin{gathered} =2脳[1-0.95] \\ =2脳0.05 \\ =0.1 \end{gathered}$$

As a result, the value of $p=0.10$, indicating that the sample proportion probability is not equal to $0.467$, but rather $0.467$is $0.10$. As a result, the normal distribution curve depicts the same.

The null hypothesis is not rejected since the alpha value is $0.05$and the p-value is bigger than the alpha value. We don't have enough evidence to say that the proportion of girls born in China isn't $46.7\%$because the null hypothesis isn't rejected.

Let's calculate the $95\%$confidence interval now:

=$p^{鈭�}卤z$

$$\begin{gathered} =0.4卤0.0784 \\ =(0.3216,0.4784) \end{gathered}$$

As a result, the $95\%$confidence level shows that the proportion of Chinese girls born falls between $32.16\%$and $47.84\%$. Let's use the normal distribution curve to depict the same.