Quiz #3

• Parameter: a numerical measure of a population that is almost always unknown and must be estimated.
• Sample statistic: a numerical descriptive measure of a sample.
• Sampling distribution: the probability distribution of a sample statistic.
• Point estimator: a statistic that can be regarded as a sensible value for a parameter.
• Unbiased estimate: a statistic where the mean is equal to the population parameter.
• Biased estimate: a statistic where the mean is not equal to the population parameter.
• Target parameter: the unknown population parameter of interest.
• Interval estimator/confidence interval: a formula that tells us how to use the sample data to calculate an interval that estimates the target parameter.
• Confidence coefficient: the probability that an interval estimator encloses the population parameter.
• Confidence level: the confidence coefficient expressed as a percentage.
• True/False: a point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate for the population parameter.

  True
• The Central Limit Theorem is important to statistics because ___.

  For a large n value, it says the sampling distribution of the sample mean is approx. normal, regardless of the population.
• This is the symbol for the standard deviation of the sampling distribution.

  
• The sampling distribution is generated by repeatedly taking samples of size n and computing the sample means.
• This is the symbol for the mean of the sampling distribution.

  
• The sampling distribution is approx. normal whenever the sample size is sufficiently large (n>30).
• The Central Limit Theorem allows us to disregard the shape of the population distribution when working with the sampling distribution of the sample mean.
• True/False: The standard error of the sampling distribution of the sample mean is equal to the standard deviation of the population.

  False
• True/False: The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

  False
• This parameter represents the quantitative mean/average.

  
• This parameter represents the qualitative proportion/fraction/percentage/rate.

  
• At a confidence level of 90%, z_α/2 = 1.645
• At a confidence level of 95%, z_α/2 =1.96
• At a confidence level of 98%, z_α/2 =2.326
• At a confidence level of 99%, z_α/2 = 2.575
• Explain what the phrase 95% confident means when we interpret a 05% confidence interval for μ.

  In repeated sampling, 95% of similarity constructed intervals contain the value of the population mean.
• The Central Limit Theorem states that the sampling distribution of the sample mean is approx. normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

  The sample size must be large (at least 30).
• True/False: The minimum-variance unbiased estimator (MVUE) has the least variance among all unbiased estimators.

  True