Which of these is not a measure of central tendency?
Standard Deviation
✓
Median
Mode
Mean
Correct Answer
Standard Deviation
Mean, Median, and Mode are all measures of central tendency, describing the center of a dataset. Standard Deviation is a measure of data dispersion (spread).
Question 2
Which of these is not a fundamental axiom of probability?
The probability of any event A is between 0 and 1 inclusive
The probability of the intersection of two independent events is the sum of their individual probabilities
✓
The probability of the sample space is 1
The probability of the union of two mutually exclusive events is the sum of their individual probabilities
Correct Answer
The probability of the intersection of two independent events is the sum of their individual probabilities
The first, second, and fourth options are fundamental axioms of probability or direct consequences. The probability of the intersection of two independent events is the product of their individual probabilities, not the sum.
Question 3
Three of these are continuous probability distributions. Which one is not?
Binomial distribution
✓
Exponential distribution
Normal distribution
Uniform distribution (over an interval)
Correct Answer
Binomial distribution
The Binomial distribution models the number of successes in a fixed number of trials, where outcomes are countable (discrete). Normal, Uniform (over an interval), and Exponential distributions are continuous probability distributions.
Question 4
Three of these are probability sampling methods. Which one is not?
Simple random sampling
Convenience sampling
✓
Cluster sampling
Stratified sampling
Correct Answer
Convenience sampling
Convenience sampling is a non-probability method where individuals are selected based on ease of access. Stratified, Simple Random, and Cluster sampling are all probability sampling methods, where each member of the population has a known, non-zero chance of being selected.
Question 5
Which of these is not directly considered an error in the context of hypothesis testing outcomes?
Type I error
Rejecting the null hypothesis when it is true
Standard error of the mean
✓
Type II error
Correct Answer
Standard error of the mean
Type I error, Type II error, and rejecting the null hypothesis when it is true (which is a Type I error) are all types of incorrect decisions or errors in hypothesis testing outcomes. The standard error of the mean is a measure of the variability of a sample mean, not an error in the decision-making process itself.
Question 6
Which of these factors, when increased, would not widen the confidence interval for a population mean?
Population standard deviation
Confidence level
Critical value (e.g., z* or t*)
Sample size
✓
Correct Answer
Sample size
Increasing the sample size typically decreases the width of a confidence interval. Increasing the confidence level, population standard deviation, or the critical value (which increases with higher confidence levels) would all lead to a wider confidence interval.
Question 7
Three of these correlation coefficients indicate a strong linear relationship. Which one does not?
0.7
-0.8
0.1
✓
-0.9
Correct Answer
0.1
The strength of a linear relationship is indicated by the absolute value of the correlation coefficient. The coefficients 0.7, -0.3, and -0.9 have absolute values of 0.7, 0.3, and 0.9, respectively. The coefficient 0.1 has an absolute value of 0.1, which is the smallest among the options, indicating the weakest linear relationship.
Question 8
Which of these is not a measure of data dispersion?
Variance
Standard Deviation
Range
Mode
✓
Correct Answer
Mode
Variance, Range, and Standard Deviation are all measures that describe the spread or dispersion of data points. Mode is a measure of central tendency, representing the most frequently occurring value.
Question 9
Which of these does not describe quantitative data?
Eye color
✓
Height in inches
Temperature in Celsius
Number of siblings
Correct Answer
Eye color
Quantitative data represents measurable quantities or counts. "Number of siblings," "Temperature in Celsius," and "Height in inches" are all quantitative. "Eye color" is categorical or qualitative data.
Question 10
Which of these is not a condition or implication of the Central Limit Theorem?
The mean of the sampling distribution of the mean is equal to the population mean
The sampling distribution of the mean will be approximately normal for a sufficiently large sample size
The population distribution itself must be normal for the theorem to apply
✓
The standard deviation of the sampling distribution of the mean (standard error) decreases as sample size increases
Correct Answer
The population distribution itself must be normal for the theorem to apply
The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the mean will be approximately normal, its mean will equal the population mean, and its standard deviation (standard error) will decrease as sample size increases. A key aspect of the CLT is that the population distribution itself does not need to be normal for the theorem to apply.
Question 11
Which of these does not represent an empirical probability?
The probability that a randomly selected person from a city will have blue eyes, based on a survey of 1000 residents
The probability of a newborn being a boy, based on historical birth records
The probability of rolling a 3 on a fair six-sided die
✓
The probability of a stock price increasing tomorrow, estimated by a financial analyst using market data
Correct Answer
The probability of rolling a 3 on a fair six-sided die
Empirical probability is based on observed frequencies or experimental results. The probabilities based on a survey, historical records, and analyst estimations are empirical or subjective. The probability of rolling a 3 on a fair six-sided die is a classical or theoretical probability, derived from logical reasoning about equally likely outcomes.
Question 12
Three of these are sample statistics. Which one is not?
Sample variance (s^2)
Population standard deviation (sigma)
✓
Sample mean (x-bar)
Sample proportion (p-hat)
Correct Answer
Population standard deviation (sigma)
A population parameter is a numerical characteristic of a population. Population standard deviation (sigma) is a parameter. Sample mean (x-bar), sample variance (s^2), and sample proportion (p-hat) are all sample statistics, which are numerical characteristics of a sample.
Question 13
Three of these test statistics use degrees of freedom. Which one does not?
F-statistic
T-statistic
Chi-squared statistic
Z-statistic
✓
Correct Answer
Z-statistic
When comparing two population means with unknown but assumed equal population standard deviations, the T-statistic is typically used. The Z-statistic is used when population standard deviations are known or for large samples. The Chi-squared statistic is for categorical data analysis (e.g., goodness-of-fit, independence), and the F-statistic is used for comparing variances or in ANOVA.
Question 14
Three of these displays summarize a single variable. Which one does not?
Scatter plot
✓
Bar chart
Histogram
Box plot
Correct Answer
Scatter plot
A scatter plot is primarily used to display the relationship between two quantitative variables. A histogram displays the distribution of a single quantitative variable. A bar chart displays frequencies for categorical data. A box plot displays the distribution of a single quantitative variable, highlighting quartiles and outliers.
Question 15
Three of these are non-probability sampling methods. Which one is not?
Quota sampling
Simple random sampling
✓
Convenience sampling
Snowball sampling
Correct Answer
Simple random sampling
Simple random sampling is a probability sampling method where every individual has an equal chance of being selected. Quota sampling, convenience sampling, and snowball sampling are all non-probability sampling methods, which do not guarantee that every member of the population has a known, non-zero chance of selection.