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Chapter 5: Problem 100

A study was recently published in Western Australia on the relationship between method of conception and prevalence of major birth defects (Hansen et al. [8]). The prevalence of at least one major birth defect among infants conceived naturally was \(4.2 \%,\) based on a large sample of infants. Among 837 infants bom as a result of invitro fertilization (IVF), 75 had at least one major birth defect. Does an unusual number of infants have at least one birth defect in the IVF group? Why or why not? (Hint: Use an approximation to the binomial distribution.)

Short Answer

Expert verified
No, the number of birth defects in the IVF group is unusually high, as indicated by a very high Z-score (6.86).

Step by step solution

01

Understand the Problem

We are given the probability of a major birth defect in naturally conceived infants, which is 4.2%, and the data for 837 IVF infants with 75 having major birth defects. The task is to determine if the number of birth defects in the IVF group is unusual.
02

Define the Null Hypothesis

The null hypothesis assumes that the rate of major birth defects in IVF infants is the same as that of naturally conceived infants. Thus, under the null hypothesis, the probability of a major birth defect, \( p \), is 0.042.
03

Calculate Expected Number of Birth Defects

With IVF infants sample size \( n = 837 \), we calculate the expected number of birth defects using the formula \( np \). \[ np = 837 \times 0.042 = 35.154 \]
04

Determine Variance and Standard Deviation

The variance for a binomial distribution is \( np(1-p) \). Calculate the variance and the standard deviation: \[ \text{Variance} = 837 \times 0.042 \times (1-0.042) = 33.691 \] \[ \text{Standard Deviation} = \sqrt{33.691} \approx 5.803 \]
05

Calculate Z-score

To find how unusual it is to have 75 birth defects, calculate the Z-score: \[ Z = \frac{\text{Observed} - \text{Expected}}{\text{Standard Deviation}} = \frac{75 - 35.154}{5.803} \approx 6.86 \]
06

Interpret the Z-score

A Z-score of 6.86 is extremely high, indicating that observing 75 or more birth defects is highly unlikely under the null hypothesis.

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Key Concepts

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

Hypothesis Testing
Hypothesis testing is a fundamental concept in statistics, often used in biostatistics to draw conclusions from data. It's like a formal tool to check if the observed results differ significantly from what was expected. In our context, it helps to determine whether IVF births lead to more birth defects compared to natural conceptions.

Here's the basic structure:
  • **Null Hypothesis ( H_0 ):** This is the default hypothesis that states there is no effect or no difference. For this study, it means that IVF and natural conception results in the same rate of birth defects.
  • **Alternative Hypothesis ( H_a ):** This hypothesis suggests there is a difference. Here, it would mean the birth defect rate is higher in IVF births.
Hypothesis testing involves calculating a statistic from your data and then assessing this statistic's significance compared to a threshold (often called the alpha level). In this case, calculating the Z-score is part of this process to understand if 75 IVF birth defects are statistically unusual.
Binomial Distribution
The binomial distribution is crucial for any situation where there are only two possible outcomes for each trial, which we're examining in this study: whether an infant does or does not have a major birth defect.

This distribution is defined by two parameters:
  • **The number of trials (n):** Here, it's the total number of IVF infants studied, which is 837.
  • **The probability of success (p):** For naturally conceived infants, the probability of a birth defect is 0.042 (or 4.2%).
The expected number of birth defects in IVF infants can be calculated using the formula np, where n is the total number, and p is the probability. The variance and standard deviation also fall under this distribution, helping us measure variability around the expected outcomes. In this case, the standard deviation helps determine how far-off our observed value of 75 birth defects is from what we'd expect under the null hypothesis.
Birth Defects Study
A birth defects study focuses on understanding the prevalence and potential causes of congenital disabilities in newborns. In this context, it looks specifically at infants conceived via methods like IVF compared to natural conception.

These studies involve collecting data from a large group of infants to determine how frequently birth defects occur. They help us understand whether certain factors potentially elevate the risk. For this study:
  • Researchers found 4.2% birth defect prevalence in naturally conceived infants.
  • They observed 75 of 837 infants from IVF births had major birth defects.
The study's aim is to identify if IVF conception contributes to a higher instance of birth defects. This could have significant implications for healthcare practices and parental advice.
IVF vs Natural Conception
In comparing IVF (In Vitro Fertilization) to natural conception, researchers aim to determine if there are health differences in offspring resulting from the two methods. IVF is a process where an egg is fertilized by sperm outside the body and then implanted in the womb.

The key inquiries in studies involving these two methods of conception include:
  • Does the environment of conception - lab versus natural - affect infant health outcomes?
  • Are there specific risks associated with IVF that parents should consider?
By examining differences, especially in birth defect prevalence, the study from Western Australia seeks to uncover if IVF could be a contributing factor to higher birth defect rates. Their findings were significant enough to show that in their sample, IVF infants exhibited a statistically larger number of birth defects than those conceived naturally. Such insights can guide future research and influence fertility treatment practices.

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Most popular questions from this chapter

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