#1
1. In a standard deck of playing cards, what is the probability of drawing a heart?
1/4
ExplanationThere are 4 suits in a deck, and 1 of them is hearts, so the probability is 1/4.
#2
6. If the probability of event A is 0.4 and the probability of event B is 0.6, what is the probability of both events A and B occurring (assuming independence)?
0.24
ExplanationMultiply the probabilities of independent events to find the joint probability.
#3
11. In a binomial distribution, what are the parameters 'n' and 'p'?
Number of trials and probability of success
Explanation'n' is the number of trials, and 'p' is the probability of success in each trial.
#4
16. What is the formula for calculating the standard error of the mean?
Standard deviation / Square root of sample size
ExplanationThe standard error of the mean is the standard deviation divided by the square root of the sample size.
#5
21. What is the purpose of the F-test in analysis of variance (ANOVA)?
To test the equality of means across multiple groups
ExplanationThe F-test in ANOVA compares variances to assess if means across multiple groups are equal.
#6
2. What is the formula for calculating the mean (average) of a set of numbers?
Sum of numbers / Number of numbers
ExplanationTo find the mean, add up all numbers and divide by the total count.
#7
3. In a normal distribution, what percentage of data falls within one standard deviation of the mean?
68%
ExplanationApproximately 68% of data falls within one standard deviation of the mean in a normal distribution.
#8
7. What is the purpose of a p-value in hypothesis testing?
To quantify the strength of the evidence against the null hypothesis
ExplanationA p-value assesses the evidence against the null hypothesis; lower values suggest stronger evidence.
#9
8. If the variance of a dataset is 25, what is the standard deviation?
10
ExplanationThe standard deviation is the square root of the variance; in this case, √25 = 10.
#10
12. What is the central limit theorem?
The distribution of sample means approaches a normal distribution as the sample size increases
ExplanationAs sample size increases, the distribution of sample means becomes more normal, regardless of the population distribution.
#11
13. In regression analysis, what does the coefficient of determination (R-squared) represent?
The proportion of the variance in the dependent variable explained by the independent variable(s)
ExplanationR-squared indicates the percentage of variation in the dependent variable explained by the independent variable(s).
#12
17. In a chi-squared test, what does the p-value indicate?
The probability of observing the data if the null hypothesis is true
ExplanationA chi-squared test p-value assesses the likelihood of observing the data if the null hypothesis is true.
#13
4. What is the difference between correlation and causation in statistical analysis?
Correlation does not imply causation
ExplanationWhile correlated variables may change together, correlation does not prove one causes the other.
#14
5. What is the significance level typically set at in hypothesis testing?
0.05
ExplanationA common significance level is 0.05, indicating a 5% chance of rejecting the null hypothesis when it's true.
#15
9. What is the formula for calculating the probability density function (PDF) of a continuous random variable?
f(x) = dF(x)/dx
ExplanationThe PDF represents the derivative of the cumulative distribution function.
#16
10. In statistical terms, what does 'Type II error' refer to?
Incorrectly failing to reject a false null hypothesis
ExplanationType II error occurs when one fails to reject a false null hypothesis.
#17
14. What is the purpose of a confidence interval in statistics?
To estimate the range within which the true population parameter is likely to fall
ExplanationA confidence interval provides a range of values within which the true population parameter is likely to lie.
#18
15. What is the difference between a parametric and non-parametric statistical test?
Parametric tests assume a normal distribution, while non-parametric tests do not
ExplanationParametric tests rely on assumptions of normality, while non-parametric tests make fewer or no distributional assumptions.
#19
19. What is the difference between a one-tailed and two-tailed hypothesis test?
One-tailed tests have a single critical region, while two-tailed tests have two critical regions
ExplanationIn a one-tailed test, critical region lies on one side of the distribution, while in a two-tailed test, it is split between both sides.