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Determining the Minimum Sample Size Required quiz

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  • What does the margin of error (e) represent in a confidence interval for a population mean?
    The margin of error tells us how far the confidence interval extends on either side of the sample mean, indicating the width of the interval.
  • How does increasing the sample size (n) affect the margin of error (e)?
    As the sample size increases, the margin of error decreases.
  • What is the formula for determining the minimum sample size (n) required for a given maximum margin of error (e)?
    The formula is n = (z * s / e)^2, where z is the critical z-value, s is the estimated standard deviation, and e is the margin of error.
  • Why do we always round up when calculating the minimum sample size required?
    We round up to ensure the margin of error does not exceed the maximum allowed and because sample size must be a whole number.
  • If you calculate a minimum sample size of 50.3, what value should you use and why?
    You should use 51, because rounding up ensures the margin of error stays within the required limit.
  • When estimating the minimum sample size, why do we use the z critical value instead of the t critical value?
    We use the z critical value because we do not know the degrees of freedom (since n is unknown), and for large samples, z and t values are nearly the same.
  • What is the critical z-value for a 95% confidence level?
    The critical z-value for a 95% confidence level is 1.96.
  • If the standard deviation is unknown, how can you estimate it for the sample size formula?
    You can estimate it using the range rule of thumb: standard deviation ≈ (range) / 4.
  • What is the range rule of thumb for estimating standard deviation?
    It states that the standard deviation can be estimated by dividing the range (maximum minus minimum) by four.
  • Why might you need to estimate the standard deviation when determining minimum sample size?
    Because you may not have collected the sample yet, so you can't calculate the sample standard deviation directly.
  • In the example, what values were used for the margin of error, standard deviation, and z-value?
    The margin of error was 3, the standard deviation was 12, and the z-value was 1.96.
  • What minimum sample size was calculated in the example, and what was the final answer after rounding?
    The calculated sample size was approximately 61.47, and after rounding up, the answer was 62.
  • What two pieces of information are needed to find the t critical value for a confidence interval?
    You need the confidence level and the degrees of freedom (n - 1).
  • Why is it important to not round down when determining the minimum sample size?
    Rounding down could result in a margin of error that is too large, exceeding the maximum allowed.
  • What should you do if prior information about the standard deviation is not available?
    Use the range rule of thumb to estimate the standard deviation by dividing the estimated range by four.