In Exercises 21-28, find the probability and answer the questions.


YSORT Gender Selection MicroSort’s YSORT gender selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort’s YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability of a boy being born using the YSORT gender selection technique. Probability is calculated as the ratio of favorable outcomes to the total number of outcomes.
2. Step 2: Identify the favorable outcomes and total outcomes. From the problem, there are 239 baby boys (favorable outcomes) and 52 baby girls. The total number of births is the sum of boys and girls: 239 + 52.
3. Step 3: Write the formula for probability. The probability of a boy being born is given by: \( P(\text{boy}) = \frac{\text{Number of boys}}{\text{Total number of births}} \). Using MathML, this can be expressed as: $\frac{239}{291}$
4. Step 4: Interpret the probability value. Once the probability is calculated, compare it to 0.5 (the probability of having a boy without any gender selection technique). If the calculated probability is significantly greater than 0.5, it suggests that the YSORT technique is effective in increasing the likelihood of a boy being born.
5. Step 5: Consider statistical significance. To determine if the technique is truly effective, additional statistical tests (e.g., hypothesis testing) may be required to assess whether the observed probability is significantly different from 0.5, accounting for sample size and variability.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it is calculated by dividing the number of favorable outcomes (baby boys) by the total number of outcomes (total births). Understanding probability is essential for determining the effectiveness of the YSORT method in increasing the likelihood of having a boy.

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship observed in data is not due to random chance. In evaluating the effectiveness of the YSORT method, one must consider whether the observed ratio of boys to girls is significantly different from the expected ratio in a natural birth scenario, typically around 1:1. This helps in assessing the true impact of the technique.

Sample Size

Sample size is the number of observations or data points collected in a study. A larger sample size generally provides more reliable estimates of probabilities and reduces the margin of error. In this case, the sample size of 291 births is crucial for determining the reliability of the probability calculated for boys being born using the YSORT method.