ST 311 Exam 1

What is a Simple Random Sample (SRS)?

Every individual in the population has the same chance of being chosen.

What is a Stratified Sample?

Population is divided into strata (groups) and random samples are taken from each group.

What is a Cluster Sample?

Population is split into clusters, and entire clusters are randomly selected.

What is a Convenience Sample?

Choosing individuals easiest to reach; usually biased.

What is Undercoverage bias?

When some groups in the population are left out of the sampling process.

What is Non-response bias?

When selected individuals do not respond, leading to bias.

What is Response bias?

When respondents do not answer truthfully or question wording affects answers.

What is the difference between an Experiment and an Observational Study?

Experiment = researcher imposes treatment. Observational study = only observing/recording.

What is a Confounding Variable?

A hidden variable that influences both the explanatory and response variable.

Categorical vs Quantitative Variables?

Categorical = groups/labels. Quantitative = numerical values.

Discrete vs Continuous Variables?

Discrete = countable (e.g., # of pets). Continuous = measurable (e.g., weight).

How does skew affect mean vs median?

Right skew: mean > median. Left skew: mean < median.

What does the box in a boxplot represent?

The middle 50% of data (Q1 to Q3).

What is Standard Deviation?

A measure of spread around the mean. Larger SD = more spread

What is the Z-score formula?

z = (x - µ) / σ

What is considered unusual in z-scores?

Values with |z| > 2 are unusual.

What is the Empirical Rule?

68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD.

What is a Parameter vs a Statistic?

Parameter = population measure (µ, p). Statistic = sample measure

What is the Central Limit Theorem?

For large n, the sampling distribution of the mean is approximately Normal

What are the conditions of a Binomial distribution?

Fixed n, two outcomes, constant p, independent trials.

What is Expected Value?

The long-run average of a random variable over many trials

When is a value unusual?

If it is more than 2 SD away from the mean or has a z-score beyond ±2.

If population is skewed but sample size is large, what is the shape of the sampling distribution of the mean?

Approximately Normal, due to the Central Limit Theorem.

When should you use the median instead of the mean?

When the data is skewed or has strong outliers, since the median is more resistant to extremes.

How does sample size affect the standard deviation of the sample proportion?

Larger sample sizes decrease the standard deviation of the sampling distribution.

Which graphs are appropriate for continuous, skewed data?

Histogram, Boxplot, or Dot plot. Bar charts are for categorical data.

For a Normal distribution, what is the best measure of spread?

Standard deviation, because it describes the typical distance from the mean

Which measure of center is best when data is skewed?

The median, because it is less affected by extreme values compared to the mean.

What does a Z-score tell us?

How many standard deviations a value is away from the mean. z = (x - µ)/σ.