#1
What does the term 'probability' refer to in statistics?
A measure of how likely it is that some event will occur
ExplanationLikelihood of event occurrence.
#2
Which distribution is known as the 'bell curve'?
Normal distribution
ExplanationSymmetric bell-shaped distribution.
#3
Which probability distribution is used for the number of successes in a fixed number of independent Bernoulli trials?
Binomial distribution
ExplanationDistribution for successes in Bernoulli trials.
#4
What is the expected value (mean) of a standard normal distribution?
0
ExplanationMean value of standard normal distribution.
#5
Which distribution is used to model the time between events in a Poisson process?
Exponential distribution
ExplanationModel for time between Poisson events.
#6
What does the Central Limit Theorem state?
The sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, regardless of the shape of the population distribution.
ExplanationSample means approach normal distribution with large samples.
#7
In a hypothesis test, what is the purpose of the p-value?
To measure the probability that the observed data occurred by chance under the assumption that the null hypothesis is true
ExplanationProbability of observed data under null hypothesis.
#8
Which of the following is a characteristic of the Poisson distribution?
Used for counting occurrences in a fixed interval of time or space
ExplanationCounting occurrences in fixed intervals.
#9
In the context of hypothesis testing, what is a Type I error?
Rejecting the null hypothesis when it is true
ExplanationFalse positive - rejecting true null hypothesis.
#10
What is the shape of the chi-square distribution?
Skewed to the right
ExplanationRight-skewed distribution shape.
#11
What distinguishes the t-distribution from the normal distribution?
The t-distribution is symmetric and bell-shaped, but has thicker tails, meaning it is more prone to producing values that fall far from its mean.
ExplanationThicker tails compared to normal distribution.
#12
What does the law of large numbers state?
The probability of an event approaches its theoretical probability as the number of trials increases
ExplanationEvent probability converges to theoretical probability.
#13
What is the primary difference between parametric and non-parametric statistical tests?
Parametric tests assume underlying statistical distributions, while non-parametric tests do not.
ExplanationDependency on underlying distribution assumption.
#14
In regression analysis, what does the R-squared value represent?
The proportion of the variance in the dependent variable that is predictable from the independent variable(s).
ExplanationPredictability of variance in dependent variable.