Questions and Answers
Describe how the variability of the distribution changes as the sample size increases.
As the sample size increases, the variability decreases.
What is the standard deviation of a sampling distribution called?
Standard error
What is a sampling distribution?
Probability distribution for a sample statistic
The value zc is a value from the standard normal distribution such that P(-zc < z < zc) = c.
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The point estimate for the population mean μ of an x distribution is x, computed from a random sample of the x distribution.
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Every random sample of the same size from a given population will produce exactly the same confidence interval for μ.
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A larger sample size produces a longer confidence interval for μ.
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If the original x distribution has a relatively small standard deviation, the confidence interval for μ will be relatively short.
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If the sample mean x of a random sample from an x distribution is relatively small, when the confidence level c is reduced, the confidence interval for μ becomes shorter.
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Study Notes
Variability and Sample Size
- Increased sample size leads to decreased variability in distribution.
Standard Error
- The standard deviation of a sampling distribution is referred to as the standard error.
Sampling Distribution
- A sampling distribution is the probability distribution associated with a sample statistic.
Critical Values and Normal Distribution
- Critical value zc is derived from the standard normal distribution and encloses an area of P(-zc < z < zc) = c.
Point Estimate for Population Mean
- The point estimate for the population mean (μ) is denoted as x, calculated from a random sample and remains consistent across the population.
Confidence Intervals and Random Samples
- Not all random samples of the same size yield identical confidence intervals for μ; variations in sample values lead to different intervals.
Sample Size and Confidence Interval Length
- Larger sample sizes do not result in longer confidence intervals for μ; they shorten the confidence interval due to reduced maximal error.
Standard Deviation and Confidence Interval
- A lower original standard deviation (σ) results in a relatively shorter confidence interval for the population mean (μ).
Confidence Level Reduction and Interval Length
- When the confidence level (c) decreases, the confidence interval for μ shortens, even if the sample mean (x) remains small; this is due to a decrease in maximal error estimate.
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Description
This quiz covers fundamental concepts in statistics, including variability, standard error, and sampling distributions. Test your understanding of how sample size impacts distribution and key statistical terms. Perfect for students looking to reinforce their statistical knowledge.
