#1
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
In a normal distribution, what percentage of data falls within one standard deviation of the mean?
Approximately 68%
Approximately 95%
Approximately 99.7%
Approximately 50%
#7
Which of the following best describes a uniform distribution?
The probability of all outcomes is the same across the distribution.
Outcomes follow a bell-shaped curve.
The distribution describes the time between random events.
Outcomes taper off symmetrically from the mean.
#8
What is the null hypothesis in a statistical test?
The hypothesis that there is a significant difference between groups
The hypothesis that there is no effect or no difference
The hypothesis that is tested by the alternative hypothesis
The hypothesis that predicts the experimental outcome
#9
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.
#10
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
#11
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
#12
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
#13
What is the shape of the chi-square distribution?
Symmetric
Skewed to the right
Skewed to the left
Uniform
#14
What does the 'degrees of freedom' refer to in the context of the t-distribution?
The number of categories minus one
The number of trials in a binomial experiment
The sample size minus one
The number of independent observations minus the number of parameters estimated
#15
For which of the following scenarios would a Poisson distribution be most appropriate?
Number of students arriving at a cafeteria every hour
Height of students in a high school
Number of heads in 100 coin flips
Time it takes to run a marathon
#16
What does it mean if a confidence interval for a mean difference includes 0?
There is definitely no difference between the means.
There is a significant difference between the means.
It is uncertain if there is a meaningful difference between the means.
0 is the mean difference between the two samples.
#17
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.
#18
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
#19
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.
#20
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.
The slope of the regression line.