STATS

What is the standard deviation of a sampling distribution called?

standard error

Describe how the variability of the distribution changes as the sample size increases.

As the sample size increases, the variability decreases.

True or false? A larger sample size produces a longer confidence interval for μ.

False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.

True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for μ.

False. Different random samples may produce different x values, resulting in different confidence intervals.

What is a sampling distribution?

Probability distribution for a sample statistic

True or false? 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.

True. As the level of confidence decreases, the maximal error of estimate decreases.

True or false? If the original x distribution has a relatively small standard deviation, the confidence interval for μ will be relatively short.

True. As σ decreases, E decreases, resulting in a shorter confidence interval.

True or false? The value zc is a value from the standard normal distribution such that P(-zc < z < zc) = c.

True. By definition, critical values zc are such that 100c% of the area under the standard normal curve falls between -zc and zc.

True or false? The point estimate for the population mean μ of an x distribution is x, computed from a random sample of the x distribution.

True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution decreases as n increases