#1
What is the median of the following dataset: 10, 15, 20, 25, 30?
#2
Which of the following is a measure of central tendency?
Standard deviation
Range
Variance
Mean
#3
What is the purpose of regression analysis in statistics?
To analyze relationships between variables
To calculate the mean
To find the mode
To measure dispersion
#4
Which of the following is NOT a measure of dispersion?
Range
Variance
Standard deviation
Mean
#5
What is the formula to calculate the coefficient of determination (R-squared) in linear regression?
1 - (SSR / SST)
1 - (SSE / SSR)
1 - (SST / SSR)
1 - (SSE / SST)
#6
Which statistical test is appropriate for comparing the means of more than two independent groups?
T-test
Chi-squared test
ANOVA
Paired t-test
#7
What does the p-value represent in hypothesis testing?
Probability of making a Type I error
Probability of making a Type II error
Probability of observing the data given that the null hypothesis is true
Probability of rejecting the null hypothesis when it is true
#8
What is the formula to calculate the standard deviation of a population?
sqrt(sum((x - x̄)^2) / n)
sqrt(sum((x - x̄)^2) / (n - 1))
sum((x - x̄)^2) / n
sum((x - x̄)^2) / (n - 1)
#9
In hypothesis testing, what does a Type II error refer to?
Incorrectly rejecting a true null hypothesis
Incorrectly failing to reject a false null hypothesis
Incorrectly accepting a true null hypothesis
Incorrectly accepting a false null hypothesis
#10
What is the purpose of the chi-squared test?
To test for the equality of means of two populations
To test for the independence of two categorical variables
To test for the normality of data
To test for the difference between paired observations
#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
The probability of rejecting the null hypothesis when it is true
The probability of making a Type I error
The probability of making a Type II error
#12
Which distribution is used to model the time until an event occurs?
Normal distribution
Binomial distribution
Poisson distribution
Exponential distribution
#13
Which distribution is used to describe the number of successes in a fixed number of independent Bernoulli trials?
Normal distribution
Binomial distribution
Poisson distribution
Exponential distribution
#14
What does the term 'confidence interval' represent in statistics?
A range of values within which the true population parameter is estimated to fall
A range of values within which the sample mean is expected to fall
A measure of the variability of the data
A measure of the central tendency of the data
#15
What is the primary objective of a hypothesis test?
To prove that the null hypothesis is true
To estimate population parameters
To make predictions about future outcomes
To assess evidence against a null hypothesis
#16
What is the purpose of hypothesis testing in statistics?
To summarize data
To estimate population parameters
To test a claim about a population parameter using sample data
To measure the variability of the 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 false null hypothesis, while Type II error is the probability of accepting a true null hypothesis
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
Type I error is the probability of accepting a false null hypothesis, while Type II error is the probability of accepting a true null hypothesis
Type I error is the probability of rejecting a true null hypothesis, while Type II error is the probability of accepting a false null hypothesis