#1
What is the median of the following dataset: 10, 15, 20, 25, 30?
22.5
ExplanationMedian is the middle value when data is arranged in ascending order.
#2
Which of the following is a measure of central tendency?
Mean
ExplanationMean represents the average of a dataset.
#3
What is the purpose of regression analysis in statistics?
To analyze relationships between variables
ExplanationRegression analysis investigates the dependence of one variable on one or more other variables.
#4
Which of the following is NOT a measure of dispersion?
Mean
ExplanationMean is a measure of central tendency, not dispersion.
#5
What is the formula to calculate the coefficient of determination (R-squared) in linear regression?
1 - (SSE / SST)
ExplanationR-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
#6
Which statistical test is appropriate for comparing the means of more than two independent groups?
ANOVA
ExplanationANOVA (Analysis of Variance) assesses whether there are statistically significant differences between the means of three or more independent groups.
#7
What does the p-value represent in hypothesis testing?
Probability of observing the data given that the null hypothesis is true
ExplanationP-value indicates the likelihood of obtaining observed results under the assumption that the null hypothesis is true.
#8
What is the formula to calculate the standard deviation of a population?
sqrt(sum((x - x̄)^2) / n)
ExplanationStandard deviation measures the dispersion of data points from the mean.
#9
In hypothesis testing, what does a Type II error refer to?
Incorrectly failing to reject a false null hypothesis
ExplanationType II error occurs when a false null hypothesis is not rejected.
#10
What is the purpose of the chi-squared test?
To test for the independence of two categorical variables
ExplanationChi-squared test determines whether there is a significant association between two categorical variables.
#11
What does the term 'p-value' represent in statistical hypothesis testing?
The probability of observing the data given that the null hypothesis is true
ExplanationP-value quantifies the strength of evidence against the null hypothesis.
#12
Which distribution is used to model the time until an event occurs?
Exponential distribution
ExplanationExponential distribution models the time between independent events occurring at a constant average rate.
#13
Which distribution is used to describe the number of successes in a fixed number of independent Bernoulli trials?
Binomial distribution
ExplanationBinomial distribution models the number of successes in a fixed number of independent trials with a constant probability of success.
#14
What does the term 'confidence interval' represent in statistics?
A range of values within which the true population parameter is estimated to fall
ExplanationConfidence interval provides a range of values likely to contain the true population parameter.
#15
What is the primary objective of a hypothesis test?
To assess evidence against a null hypothesis
ExplanationHypothesis testing evaluates whether observed data deviates from what is expected under a null hypothesis.
#16
What is the purpose of hypothesis testing in statistics?
To test a claim about a population parameter using sample data
ExplanationHypothesis testing evaluates whether a hypothesis about a population parameter is supported by sample data.
#17
What is the difference between Type I and Type II errors in hypothesis testing?
Type I error is the probability of rejecting a true null hypothesis, while Type II error is the probability of rejecting a false null hypothesis
ExplanationType I error occurs when a true null hypothesis is incorrectly rejected, while Type II error occurs when a false null hypothesis is not rejected.