Inferential Statistics Exam Review

A comprehensive set of flashcards covering essential concepts in inferential statistics to aid in exam preparation.

What is the main purpose of inferential statistics?

To make inferences or predictions about a population based on sample data.

What does inferential statistics involve?

Drawing conclusions from data.

What is inferential statistics based on?

Random sampling.

Which is an example of inferential statistics?

Estimating the average GPA of all university students based on a sample.

What is the numerical summary of a population called?

Parameter.

What is the numerical summary of a sample referred to as?

Statistic.

What does the sampling error refer to?

The difference between a sample statistic and the population parameter.

What is the purpose of hypothesis testing?

To test whether a claim about a population parameter is supported by sample data.

What does the null hypothesis (H₀) typically state?

There is no significant difference or effect.

What does the alternative hypothesis (H₁) state?

There is a difference or effect present.

What does the p-value represent?

The probability of seeing your data (or more extreme data) if the null hypothesis were true.

What should you do if p < 0.05?

Reject the null hypothesis.

What does a confidence interval provide?

A range of values likely to include the population parameter.

What does an alpha level (α) of .05 represent?

The 5% probability of making a Type I error.

What does a smaller standard error indicate?

The sample mean is a more precise estimate of the population mean.

What are the measures of central tendency?

Mean, Median, and Mode.

How is the mean defined?

The sum of all observations divided by the number of observations.

What best describes the median?

The midpoint of a dataset when arranged in order.

What is the mode?

The most frequently occurring value in a dataset.

What happens when all values in a dataset are the same?

Mean, Median, and Mode will be equal.

In a positively skewed distribution, which relationship holds?

Mode < Median < Mean.

In a negatively skewed distribution, which relationship holds?

Mean < Median < Mode.

What is the effect of extreme values on the mean?

The mean is most affected by extreme values (outliers).

When is the median especially useful?

When there are extreme outliers.

What is the mode most appropriate for?

Nominal (categorical) data.

What happens if you remove a number from a dataset with a known mean?

You can determine the value removed based on the new mean.

Which statistic is calculated as the highest value minus the lowest value?

Range.

What does variance measure?

The average squared deviation from the mean.

What does standard deviation represent?

The square root of the variance.

What indicates that data is clustered closely to the mean?

A small standard deviation.

What indicates high variability in data?

A large standard deviation.

What does a normal distribution look like?

It is symmetrical and bell-shaped.

In a normal distribution, what is true about the mean, median, and mode?

All are equal.

What is the empirical rule?

Approximately 68%, 95%, and 99.7% of data fall within 1, 2, and 3 standard deviations of the mean.

What characterizes a positively skewed distribution?

The tail is longer on the right.

What is skewness?

A measure of the symmetry or asymmetry of a distribution.

What does kurtosis measure?

The peakness or flatness of a distribution.

What does a normal distribution's kurtosis value equal?

3.

What is the null hypothesis symbol?

H₀.

What is the default assumption in hypothesis testing?

The null hypothesis is true.

What is a one-sample t-test used for?

To compare a sample mean with a known or hypothesized population mean.

What does a large t-value indicate?

There is a large difference between sample and population means.

What does a paired-sample t-test compare?

The means of the same group measured twice.

What is the key difference between population and sample z-scores?

Population z-scores use μ and σ; sample z-scores use x̄ and s.