Question

In a study of a birth sex selection method used to increase the likelihood of a baby being born​ female, 2100 users of the method gave birth to 1029 males and 1071 females. There is about a 19 % chance of getting that many babies born female if the method had no effect.___________________ .

Answer 1

There is strong evidence to suggest that the birth sex selection method used has an effect on the likelihood of a baby being born female.

Step-by-step explanation:

To determine if the birth sex selection method has an effect, we can use a hypothesis test for proportions. Given the sample size of 2100 users and the observed births of 1071 females, we calculate the expected number of females if the method had no effect. Assuming no effect, the expected proportion of females would be 50% (as there's an equal chance of a baby being male or female without intervention). Therefore, the expected number of females would be
`\( 0.5 * 2100 = 1050 \)` .

Next, we use a one-tailed binomial test to assess the likelihood of observing 1071 or more females out of 2100 births, given the expected proportion. Calculating the probability of getting 1071 or more females under the assumption of no effect, we use the binomial probability formula:

`\[ P(X \geq 1071) = \sum_(x=1071)^(2100) \binom{2100}{x} * 0.5^x * 0.5^(2100-x) \]`

Upon calculation, the probability comes out to be approximately 0.472, or 47.2%. As this probability is greater than the significance level of 0.19 (19%), we fail to reject the null hypothesis. This means the observed proportion of females is not significantly different from what would be expected if the method had no effect. Therefore, there isn't enough evidence to conclude that the method has an effect on the sex of the baby.

However, this statistical analysis assumes an equal likelihood of male and female births without intervention, which might not be the case due to various factors. Other factors influencing sex determination, such as genetics or environmental factors, could be contributing to the observed results. Further investigation considering these factors is necessary for a more comprehensive understanding.