What is a population in statistics?
The set of individuals or objects being studied.
What is a sample in statistics?
A subset of the population.
What is a statistical variable?
A characteristic or property of interest of a population.
How are statistical variables broadly classified?
As categorical or numerical.
What are the two types of categorical variables?
Nominal and ordinal.
How are numerical variables further classified?
As discrete or continuous.
How is the median identified in ordered data?
It is the middle data point.
What does variance measure around the mean?
Dispersion.
What is variance the expected value of?
Squared deviations from the mean.
What does the sample space of a random experiment contain?
All possible outcomes.
What does a random variable assign to each possible outcome?
A number.
What probability does a probability mass function give for each value?
The probability that a discrete random variable takes that value.
How is the expected value of a discrete random variable calculated?
As the probability-weighted average of its possible values.
What shape does a normal distribution have?
Bell-shaped.
What does the mean determine in a normal distribution?
The curve’s position on the horizontal axis.
How does increasing variance affect a normal curve when the mean is unchanged?
It becomes flatter and more spread out.
What does a standardized value indicate about an observation?
How many standard deviations it lies above or below the mean.
How is standard deviation related to variance?
It is the square root of the variance.
What does standard deviation measure?
Dispersion around the expected value.
What does a 95% confidence procedure achieve across repeated samples?
Approximately 95% of its intervals contain the true parameter.
What does a 95% confidence procedure not imply about a particular computed interval?
It does not imply a 95% probability that the interval contains the parameter.
What divisor makes the sample variance an unbiased estimator of population variance?
How do Student’s t-distributions compare with the standard normal distribution’s tails?
Student’s t-distributions have heavier tails.
How does a Student’s t-distribution’s central 95% interval compare with the standard normal’s?
It is wider.
Under what sampling conditions is the classical t-interval exact?
For an independent random sample from a normally distributed population.
What role does the null hypothesis H₀ play in a hypothesis test?
It is the default statement, rejected only when the sample provides sufficient evidence against it.
What claim does the alternative hypothesis Hₐ represent?
The competing research claim to which the burden of proof is assigned.
What is a Type I error in hypothesis testing?
Erroneously rejecting a true H₀.
What is a Type II error in hypothesis testing?
Erroneously failing to reject H₀.
What does the significance level α limit in hypothesis testing?
The maximum tolerated probability of rejecting H₀ when H₀ is true.
When does a hypothesis test reject H₀ based on its p-value?
When the p-value is less than or equal to α.
How is the p-value defined under H₀?
The probability of observing a test statistic at least as extreme as the observed statistic in the direction or directions specified by Hₐ.
What does the 95% interval [0.34, 3.71] indicate about μ₁ and μ₂?
It provides evidence that μ₁ exceeds μ₂.
What is μtreatment − μcontrol called in a randomized controlled experiment?
The average treatment effect.
What range can a discrete numerical variable have?
A finite or countably infinite range.
What kind of range is modeled for a continuous variable?
An uncountable range.
What is the mode of a data set?
The most frequent value or observation.
How is the range calculated?
Maximum value minus minimum value.
How is the interquartile range calculated?
Third quartile minus first quartile.
Which symbol denotes the population mean?
Which symbol denotes the sample mean?
What does a standardized value of mean?
The observation is two standard deviations below the mean.
How is the observed estimate of population proportion π calculated from 8 fraudulent transactions among 200?
0.04.
How does a 99% confidence interval compare in width with a 95% interval for the same sample?
It is approximately 31% wider and less precise.
What happens to the standard error when sample size is multiplied by 4 and π remains unchanged?
It is divided by 2.
What distribution approximately describes the sample proportion for a sufficiently large random sample?
A normal distribution.
Why does sample variance have degrees of freedom?
The deviations from the sample mean sum to zero, leaving only independently variable deviations.
What distribution does the t-distribution approach as its degrees of freedom increase?
The standard normal distribution.
How does a t-based confidence interval generally compare in width with its corresponding z-based interval?
It is generally wider.
Why is a t-based confidence interval generally wider than its corresponding z-based interval?
The t-distribution’s heavier tails produce a larger critical value.
What does an observed test statistic of 2.37 mean?
The observed difference is 2.37 estimated standard errors above zero.
What determines the standard error for two means with unknown, potentially unequal variances?
The separate sample variances and sample sizes.
What does the 95% interval [$5.84, $17.62] estimate for willingness to pay?
An increase of about $5.84 to $17.62 in willingness to pay.
How is the cumulative distribution function denoted in the course excerpt?
Answer 25 questions on Statistical Data Analysis.
1. A researcher is studying the heights of students at a university. What is the population in this study?
2. A survey measures the commuting times of 200 employees chosen from a company of 3,000 employees. What are the 200 chosen employees?
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