Binomial Distribution Practice Problems
1. The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996 31% of students reported that their mothers had graduated from college. In 2000, responses from 500 students found that 160 out of 500 mothers had graduated from college.
Research Question – Are more mothers graduating from college than previously?
- Define the population of interest.
- Define the variable of interest.
- Describe in context how this scenario is Binomial.
- Assuming only 31% of mothers graduate from college, how many of the 500 mothers in the study would you expect to have graduated from college?
- Assuming only 31% of mothers graduate from college, what is the probability of observing results at least as extreme as observed? (You’ll need to use JMP to find this.)
- Does this study provide evidence that more mothers are graduating from college than previously? Explain.
2. In 2001 a national vital statistics report indicated that about 3% of all births produce twins. Data from a large city hospital found that only 2 sets of twins were born to 200 teenage girls. Does this suggest that teenage mothers are less likely to have twins?
Research Question – Are teenage girls less likely to have twins?
- Define the population of interest.
- Define the variable of interest.
- Describe in context how this scenario is Binomial.
- Assuming only 3% of all births produce twins, how many of the 200 teenage girls in would you expect to have twins?
- Assuming only 3% of all births produce twins, what is the probability of observing results at least as extreme as observed?
- Does this study provide evidence that teenage girls are less likely to have twins? Explain.
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