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Confidence Intervals for Population Mean quiz #1

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  • What is a point estimate for the population mean (μ) when constructing a confidence interval?
    The sample mean (x̄) is used as a point estimate for the population mean (μ) when constructing a confidence interval.
  • What constant is used to calculate the 90% confidence interval for the mean when the sample size n = 50 and the population standard deviation is unknown?
    When the population standard deviation is unknown and n = 50, the constant used is the critical t value (tα/2) for 49 degrees of freedom (n-1) at a 90% confidence level.
  • What is the confidence level if the significance level α = 0.10?
    If α = 0.10, the confidence level is 1 - α = 0.90, or 90%.
  • What happens to the expected value of the sample mean (x̄) as the sample size increases?
    As the sample size increases, the expected value of the sample mean (x̄) remains equal to the population mean (μ); however, the variability (standard error) of x̄ decreases.
  • What is the distribution of the difference between sample means from two normal populations?
    The difference between sample means from two normal populations is normally distributed if both populations are normal and the samples are independent.
  • When constructing a confidence interval for a population mean, which calculations are derived from the confidence interval?
    Calculations derived from the confidence interval include the margin of error, the lower bound, and the upper bound of the interval.
  • An interval estimate is used to estimate which population parameter?
    An interval estimate is used to estimate the population mean (μ).
  • What is the approximate sampling error for a properly drawn sample of one thousand individuals?
    For a properly drawn sample of one thousand individuals, the approximate sampling error is plus or minus 3% for a 95% confidence level.
  • When using the Student's t distribution to test the population mean, what conditions must be met?
    When using the Student's t distribution to test the population mean, the sample must be random, and either the population is normal or the sample size is greater than 30.
  • How do you construct a confidence interval for a population mean when the population standard deviation is unknown?
    To construct a confidence interval for a population mean when the population standard deviation is unknown, use the sample mean as the point estimate, calculate the margin of error as tα/2 × (s/√n), where s is the sample standard deviation and tα/2 is the critical t value for n-1 degrees of freedom, then add and subtract the margin of error from the sample mean to find the interval.