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Chapter 4: Problem 26

Find the probability and answer the questions. 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?

Short Answer

Expert verified
The probability of having a boy using YSORT is approximately 0.821 (82.1%). This indicates that the technique is effective in increasing the likelihood of a boy.

Step by step solution

01

- Determine Total Births

First, find the total number of births by adding the number of boys to the number of girls. Total births = 239 boys + 52 girls = 291 births.
02

- Calculate Probability of a Boy

Next, calculate the probability of having a boy by dividing the number of boys by the total number of births. Using the formula for probability: \[ P(\text{Boy}) = \frac{\text{Number of boys}}{\text{Total number of births}} P(\text{Boy}) = \frac{239}{291} P(\text{Boy}) \approx 0.821 \]
03

- Interpret the Result

Finally, interpret the probability calculated to determine if it shows an increased likelihood of having a boy. A probability of approximately 0.821 (82.1%) is significantly higher than the natural birth ratio of boys (roughly 51%). Thus, this suggests that the YSORT technique is effective at increasing the likelihood of having a boy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Probability Calculation
Probability helps us measure the chance of a specific outcome. In the context of gender selection using MicroSort's YSORT technique, we need to measure the chance of a baby being a boy. Here鈥檚 how we break it down:
  • Firstly, we determine the total number of births. In this case, 239 boys and 52 girls add up to 291 births.
  • Next, we calculate the probability of a boy being born using the formula: \ \[P(\text{Boy}) = \frac{\text{Number of boys}}{\text{Total number of births}}\ \]
  • Substitute the values: \ \[P(\text{Boy}) = \frac{239}{291}\ \]
  • This calculation gives us approximately 0.821, or 82.1%.
The high percentage from our calculation indicates the likelihood of having a boy using YSORT is much higher than the natural probability, which is around 51%.
Gender Selection
Gender selection refers to the practice of attempting to influence the probability of a baby's gender. Techniques like MicroSort's YSORT are created to help parents choose the gender of their baby. Here's how YSORT fits in this context:
  • YSORT is designed to increase the likelihood of having a baby boy.
  • It involves sorting sperm to increase the chances of selecting the Y chromosome, which results in a male child.
  • In our example, the birth data showed 239 boys out of 291 births.
This data is a significant sample suggesting that this method has a high probability of success. Techniques like YSORT are controversial and raise ethical questions, but they aim to help parents with gender preferences.
Statistical Interpretation
Statistical interpretation involves understanding and making sense of the calculated probabilities. Let鈥檚 depart our calculation in simpler terms:
The probability of 0.821 (82.1%) for having a boy using YSORT shows that this technique is effective. Here鈥檚 how we interpret this:
  • A higher probability compared to the natural ratio (about 51%) shows a successful increase in the chances of having a boy.
  • Statistical significance is essential, and our result of 82.1% is notably higher than 51%, indicating a reliable difference.
Interpreting statistical data involves discussing the effectiveness and potential implications of the results. It gives us factual backing to state that YSORT significantly increases the likelihood of having a boy.
Birth Ratio Analysis
Birth ratio analysis involves comparing the probability of different outcomes in births. For our case using YSORT:
  • We observed 239 boys and 52 girls. These numbers compare the success rate of the technique.
  • The ratio of boys to girls in our dataset is derived by comparing 239 boys to 52 girls, which shows a higher boys' count.
  • This stark difference against the natural ratio (approximately 1:1 ratio of boys to girls) suggests the effect of the gender selection technique.
Analyzing the birth ratio helps us understand how effective the YSORT method is. It provides a clear, statistical observation that the technique works as intended to increase the likelihood of male births.

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Most popular questions from this chapter

Describe the simulation procedure. (For example, to simulate 10 births, use a random number generator to generate 10 integers between 0 and 1 inclusive, and consider 0 to be a male and 1 to be a female.) Lefties Ten percent of people are left-handed. In a study of dexterity, 15 people are randomly selected. Describe a procedure for using software or a TI- \(83 / 84\) Plus calculator to simulate the random selection of 15 people. Each of the 15 outcomes should be an indication of one of two results: (1) Subject is left-handed; (2) subject is not left-handed.

Express all probabilities as fractions. Your professor has just collected eight different statistics exams. If these exams are graded in random order, what is the probability that they are graded in alphabetical order of the students who took the exam?

Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study on the enhancing effect of coffee on long-term memory found that 35 participants given \(200 \mathrm{mg}\) of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine. a. There was a probability of 0.049 that the difference between the coffee group and the placebo group was due to chance. What do you conclude? b. A group given a higher dose of 300 mg performed better than the 200 mg group, with a probability of 0.75 that this difference is due to chance. What do you conclude?

When the horse California Chrome won the 140th Kentucky Derby, a \(\$ 2 dollars bet on a California Chrome win resulted in a winning ticket worth \)\7 dollars. a. How much net profit was made from a \(\$ 2\) win bet on California Chrome? b. What were the payoff odds against a California Chrome win? c. Based on preliminary wagering before the race, bettors collectively believed that California Chrome had a 0.228 probability of winning. Assuming that 0.228 was the true probability of a Califonia Chrome victory, what were the actual odds against his winning? d. If the payoff odds were the actual odds found in part (c), what would be the worth of a \(\$ 2\) win ticket after the California Chrome win?

Find the probability.At Least One. In Exercises \(5-12,\) find the probability. In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in \(2015 .\) )
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