APMA 3110 HW07 WebWork True/False Questions

4.9, 5.1, 5.3

True/False: Confidence level and margin of error are inversely proportional (as one increases, the other decreases) for intervals based on the same data.

False

True/False: A sample is always smaller than a population.

False

True/False: A confidence interval for a population mean is exact when the population distribution is Normal and is approximately correct when n is large in other cases.

True

True/False: A confidence interval for a population mean is always centered at x bar (sample mean).

True

True/False: The population refers to the entire collection of interest.

True

True/False: It is a standard and reasonable assumption that one will always know the standard deviation σ of a population.

False

True/False: Consider two confidence intervals for the same Normally distributed variable generated from the same sample, one with a 80% confidence level and the other with a 95% confidence level. It is possible for the two intervals to have the same margin of error.

False

True/False: The margin of error can be cut in half by increasing the sample size by a factor of four.

True

True/False: There is a different t-distribution for each sample size.

True

True/False: The sampling distribution of x bar (sample mean) depends on σ.

True

True/False: As the degrees of freedom decreases, the t distribution approaches the standard Normal distribution.

False

True/False: The spread of a t-distribution is a bit less than that of the standard Normal distribution.

False

True/False: The t-statistic differs from the z-statistic in that it uses the standard error of x bar (sample mean) rather than the standard deviation.

True

True/False: When the standard deviation of a statistic is estimated from the data, the result is called the standard error of the statistic.

True

True/False: If a simple random sample of size n is taken from a Normally distributed population with mean μ and standard deviation σ, then the sample mean x bar is Normally distributed with mean μ and variance σ/n.

False

True/False: Like the z-statistic, the t-statistic is Normally distributed.

False