#1
Which statistical distribution is commonly used to model the number of successes in a fixed number of independent Bernoulli trials?
Binomial distribution
ExplanationIt describes the number of successes in a fixed number of independent trials with the same probability of success.
#2
Which statistical test is appropriate for comparing the means of two independent groups?
Independent t-test
ExplanationIt determines if there is a significant difference between the means of two independent groups.
#3
What is the purpose of a null hypothesis in hypothesis testing?
To assert that there is no significant difference or relationship
ExplanationIt serves as a basis for comparison, assuming no effect or relationship between variables.
#4
What is the purpose of an outlier in a boxplot?
To identify extreme values in the dataset
ExplanationIt visually highlights data points that significantly differ from the bulk of the data.
#5
Which of the following is NOT a measure of variability?
Mean
ExplanationIt is a measure of central tendency, not variability, which describes how spread out the data points are.
#6
What is the fundamental principle of statistical inference?
Hypothesis Testing
ExplanationIt involves making a hypothesis about a population parameter and then using sample data to test the hypothesis.
#7
Which measure of central tendency is most affected by outliers?
Mean
ExplanationIt is heavily influenced by extreme values, pulling the value towards them.
#8
What does the term 'confidence interval' represent in statistics?
A range of values used to estimate a population parameter
ExplanationIt provides a plausible range of values for an unknown parameter based on sample data.
#9
What is the formula to calculate the variance of a sample?
Σ(x - μ)² / (n - 1)
ExplanationIt measures the dispersion of data points around the mean, adjusted for sample size.
#10
What is the formula to calculate the standard deviation of a population?
Σ(x - μ) / (n - 1)
ExplanationIt measures the average deviation of data points from the mean, adjusted for sample size.
#11
In statistical terms, what is 'p-value'?
Probability of obtaining a test statistic at least as extreme as the one observed
ExplanationIt quantifies the evidence against the null hypothesis, indicating how likely it is to observe the given data if the null hypothesis were true.
#12
What is the purpose of a Type II error in hypothesis testing?
Incorrectly failing to reject a false null hypothesis
ExplanationIt means accepting the null hypothesis when it's false, thus missing a significant result.
#13
Which of the following is NOT an assumption of linear regression?
Independence of observations
ExplanationIt assumes that observations are independent of each other, which is not a requirement for linear regression.
#14
What does the term 'statistical power' refer to?
The probability of correctly rejecting a false null hypothesis
ExplanationIt indicates the likelihood of detecting an effect or relationship when it truly exists.