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Confidence Intervals for Population Proportion quiz

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  • What is the first step before constructing a confidence interval for a population proportion?
    Verify that both the number of successes and failures are at least five.
  • How do you calculate the point estimate (p̂) for a population proportion?
    Divide the number of successes (x) by the total sample size (n).
  • What is the formula for the margin of error (e) when constructing a confidence interval for a proportion?
    e = zα/2 × sqrt[p̂(1-p̂)/n]
  • How do you find the critical z value for a given confidence level?
    Subtract the confidence level from 1, divide by 2, and use a z-table or calculator to find the corresponding z value.
  • What does a 90% confidence interval mean in the context of population proportion?
    It means we are 90% confident that the true population proportion lies within the calculated interval.
  • If you are not given p̂ when calculating minimum sample size, what value should you use and why?
    Use p̂ = 0.5 because it gives the largest required sample size for a given margin of error.
  • How do you calculate the lower and upper bounds of a confidence interval for a proportion?
    Subtract the margin of error from p̂ for the lower bound and add it to p̂ for the upper bound.
  • What is the formula to calculate the minimum sample size (n) for a desired margin of error?
    n = [zα/2 / e]^2 × p̂(1-p̂)
  • Why do you round up the sample size when calculating the minimum required n?
    Because you cannot sample a fraction of a subject, so you need a whole number.
  • What function on the TI-84 calculator is used to construct a confidence interval for a population proportion?
    Use the '1-PropZInt' or '1-Prop C Interval' function.
  • What information do you need to enter into the TI-84 to calculate a confidence interval for a proportion?
    You need the number of successes (x), sample size (n), and the confidence level.
  • If a sample of 50 customers includes 32 who prefer chocolate chip, what is p̂?
    p̂ = 32/50 = 0.64
  • What does it mean if your confidence interval for a proportion is (0.528, 0.752)?
    You are confident at the specified level (e.g., 90%) that the true population proportion is between 0.528 and 0.752.
  • Why is it important to check that both np and nq are at least 5 before constructing a confidence interval?
    This ensures the sampling distribution of p̂ is approximately normal, which is required for the interval to be valid.
  • How does increasing the sample size affect the margin of error in a confidence interval for a proportion?
    Increasing the sample size decreases the margin of error, making the confidence interval narrower.