Sampling Distributions
If a population has a mean μ and standard deviation σ, what will be true for a sampling distribution of with a sufficiently large sample size?
There is not enough information to determine the mean.
The mean will be greater than μ.
The mean will be μ.
The mean will be less than μ.
What is the purpose of using a sample in statistics?
To provide results with absolute certainty.
To estimate characteristics of a population.
To test hypotheses with no uncertainty.
To eliminate the need for data collection.
Given three different populations with unknown means and variances, under which condition would it be inappropriate to use their respective properly calculated standard deviations as estimates for their standard errors when obtaining samples?
All populations are normally distributed with known variances regardless of sample size.
Populations are not normally distributed but very large samples (n>30) are drawn from each one.
One population has an unknown but highly skewed distribution even with large sample size.
All populations have unknown variances but large samples are taken from each one.
The Central Limit Theorem is applicable to both _ and _ data.
Continuous; binary.
Continuous; discrete.
Quantitative; ordinal.
Quantitative; categorical.
When comparing standard deviations of two different means calculated from samples of sizes and where , in which scenario will these standard deviations be equal given both samples are from the same population?
When both samples have identical variances.
This scenario cannot occur since sample size affects standard deviation.
When there is no skewness or outliers present in either sample.
When both samples are drawn randomly and independently.
In hypothesis testing using z-scores where sigma is known and when increasing alpha from .01 to .05 while keeping everything else constant, how does this change affect our decision rule regarding whether or not we reject H0?
Keep rejection rate same since test statistic unaffected by alpha
Less frequent rejections as need stronger evidence against H0
Reject H0 more frequently due incorrect Type I errors increase
Can't determine without knowing specifics about alternative hypothesis
When conducting a significance test from a skewed distribution with , how does increasing variability affect Type II error rates if all other factors remain constant?
Type II error rates increase.
Type II error rates are unaffected by variability in skewed distributions.
Type II error rates remain constant.
Type II error rates decrease.

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What sequence changes occur in the sampling distribution of the sample mean when the population variance is unknown, switching from t-tests to z-tests because of larger sample sizes?
No change in sampling distribution occurs since tests rely on sample variance
Uncertainty regarding whether the distribution is skewed or not, with evidence for more mixed results
Assumption of normality becomes less critical given large samples that do not require characteristics of the underlying population
Sampling distribution becomes nearly normal as sample size increases
Where is the Central Limit Theorem generally tested on the AP Statistics exam?
On multiple-choice questions dealing with quantitative data.
On multiple-choice questions dealing with categorical data.
On free response questions dealing with quantitative data.
On free response questions dealing with categorical data.
Which measure remains unchanged as more samples are taken according to the Central Limit Theorem?
Population mean
Standard deviation of sampling distribution
Sample variance
Distribution of sample proportions