Statistical Inference and Probability Distributions Quiz
Test your knowledge with 14 questions on probability, distributions, and statistical inference. Explore topics like the central limit theorem, p-value, and more!
What does the term 'probability' refer to in statistics?
A measure of how likely it is that some event will occur
A technique to control the flow of execution
A type of loop
A method to display output
#2
Which distribution is known as the 'bell curve'?
Poisson distribution
Uniform distribution
Normal distribution
Binomial distribution
#3
Which probability distribution is used for the number of successes in a fixed number of independent Bernoulli trials?
Normal distribution
Binomial distribution
Poisson distribution
Exponential distribution
#4
What is the expected value (mean) of a standard normal distribution?
1
0
-1
The mean is not defined for a standard normal distribution
#5
Which distribution is used to model the time between events in a Poisson process?
Normal distribution
Binomial distribution
Exponential distribution
Chi-square distribution
#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.
The mean of a sample is always equal to the mean of the population.
The variance of the population can be determined by the variance of a sample.
The probability of an event is fixed and does not change with the size of the sample.
#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
To calculate the mean of the sample data
To determine the variance of the population
To establish the sample size required for the experiment
#8
Which of the following is a characteristic of the Poisson distribution?
Used for counting occurrences in a fixed interval of time or space
Symmetrical distribution
Defined by a success probability p in each trial
The mean and variance are different
#9
In the context of hypothesis testing, what is a Type I error?
Accepting the null hypothesis when it is false
Rejecting the null hypothesis when it is true
Accepting the alternative hypothesis when it is false
Rejecting the alternative hypothesis when it is true
#10
What is the shape of the chi-square distribution?
Symmetric
Skewed to the right
Skewed to the left
Uniform
#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.
The t-distribution is not symmetric, unlike the normal distribution.
The t-distribution can only be used for sample sizes greater than 30.
The t-distribution represents discrete variables, whereas the normal distribution represents continuous variables.
#12
What does the law of large numbers state?
The sample mean approaches the population mean as the sample size increases
The sample variance approaches the population variance as the sample size increases
The probability of an event approaches its theoretical probability as the number of trials increases
The variance of the sample mean decreases as the sample size increases
#13
What is the primary difference between parametric and non-parametric statistical tests?
Parametric tests are used for ordinal data, while non-parametric tests are used for nominal data.
Parametric tests assume underlying statistical distributions, while non-parametric tests do not.
Non-parametric tests can only be used when the sample size is less than 30.
Parametric tests are less powerful than non-parametric tests.
#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).
The correlation between the independent and dependent variables.
The average distance of the data points from the regression line.