In an analysis of test results from the YSORT gender selection method, 152 babies are born and it is assumed that boys and girls are equally likely, so n=152 and p=0.2.

do you have a question? and shouldnt p=0.5?

It seems there might be a slight confusion with the values provided. In the context of the YSORT gender selection method, it is more commonly assumed that the probability of having a boy (p) is 0.5 (50%) and the probability of having a girl is also 0.5. This assumption reflects the equal likelihood of each gender during natural conception.

However, in your question, you mentioned that p=0.2, suggesting that the probability of having a boy is only 0.2 (20%). If this assumption is accurate for the YSORT gender selection method you are referring to, then we can continue with the values n=152 and p=0.2.

To proceed with the analysis, it seems you are interested in understanding the statistical significance of the observed number of births. In other words, you want to determine if the number of boys and girls born significantly deviates from the expected number based on the assumed probability.

To evaluate this, we can use the binomial distribution and perform a hypothesis test. The null hypothesis (H0) would state that the observed number of boys and girls is not significantly different from the expected number, while the alternative hypothesis (H1) would suggest that there is a significant difference.

To calculate the expected number of boys and girls under the assumption that boys and girls are equally likely with p=0.2, we can multiply the probability by the total number of births (n). In this case, the expected number of boys (E_boys) would be p * n = 0.2 * 152 = 30.4, and the expected number of girls (E_girls) would also be 30.4.

To continue the analysis and perform the hypothesis test, we would need additional information, such as the actual observed number of boys and girls.