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Statistics Final Exam Concepts

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  • What is cluster sampling?

    Cluster sampling involves dividing a population into clusters, randomly selecting some clusters, and surveying every member within those clusters.

  • What is a possible bias in cluster sampling?

    Bias can occur if the clusters not chosen have different characteristics or needs than those selected.

  • How can you interpret a histogram for normality?

    A histogram suggests normal distribution if it is symmetric, bell-shaped, and unimodal.

  • What does a boxplot display?

    A boxplot displays the median, quartiles, and potential outliers of a data set, showing its spread and skewness.

  • How do you calculate range, variance, and standard deviation?

    Range = max - min; Variance = average squared deviation from mean; Standard deviation = square root of variance.

  • What does a high standard deviation indicate about data variability?

    High standard deviation indicates data points are spread out widely from the mean, showing high variability.

  • What is the complement rule in probability?

    The complement of event A, denoted P(A̅), is 1 - P(A), representing the probability that A does not occur.

  • What is the multiplication rule for dependent events?

    For dependent events A and B, P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of B given A occurred.

  • What characterizes a Poisson distribution?

    A Poisson distribution models the number of events occurring in a fixed interval with a known average rate and independent events.

  • What is a discrete random variable?

    A discrete random variable takes countable values, such as number of pages or languages spoken.

  • What is a continuous random variable?

    A continuous random variable takes any value within an interval, such as time or amount of milk produced.

  • What is a uniform distribution?

    A uniform distribution has equal probability for all values within a specified range.

  • What does the area under a normal density curve represent?

    The area to the left of a point \(x_0\) is the percentile rank, expected proportion of observations ≤ \(x_0\), and the cumulative probability.

  • Which measurement is most likely normally distributed?

    Measurements like lengths of pencils in a box are likely to follow a normal distribution.

  • What is the Central Limit Theorem?

    The sample mean distribution approaches normality as sample size increases, regardless of population distribution.

  • What is a confidence interval?

    A confidence interval estimates a population parameter with a range of values and a confidence level.

  • How to find the point estimate and margin of error from a confidence interval?

    Point estimate = midpoint of interval; Margin of error = half the width of the interval.

  • What is the chi-square distribution used for?

    Chi-square distribution is used in tests of variance and goodness-of-fit for categorical data.

  • How to determine minimum sample size for estimating standard deviation?

    Sample size depends on desired confidence level and allowable error margin relative to population standard deviation.

  • What is the null hypothesis in variance hypothesis testing?

    The null hypothesis often states that the population variance or standard deviation equals a specified value.

  • What are critical values and rejection regions in hypothesis testing?

    Critical values define boundaries; rejection regions are values where the null hypothesis is rejected.

  • What is the sign test used for in proportions?

    The sign test compares paired proportions to test if they differ significantly.

  • What is the F distribution used for?

    The F distribution is used to compare two variances in hypothesis testing.