List of top Statistics Questions

If the null hypothesis \(H_0\) is rejected when it is actually true, what type of error has been committed?
What is the degree of freedom for a Chi-square test used in a \(3 \times 4\) contingency table?
Find the limit of \( \left(1 + \frac{1}{n}\right)^n \) as \(n \to \infty\).
In a negatively skewed distribution, what is the correct relationship between the Mean, Median, and Mode?
What is the value of the integral \( \displaystyle \int_{-\infty}^{\infty} e^{-x^2}\,dx \)?
Which test is most appropriate for testing the significance of the difference between two small sample means?
A bag contains \(5\) red and \(7\) blue balls. If two balls are drawn at random, what is the probability that both are red?
If the correlation coefficient between \(X\) and \(Y\) is \(0.8\), what is the coefficient of determination?
In Simple Random Sampling Without Replacement (SRSWOR), what is the probability of selecting a specific unit at the second draw?
What is the rank of a \(3 \times 3\) identity matrix added to a \(3 \times 3\) null matrix?
In a Normal distribution, what percentage of data falls within two standard deviations of the mean?
If a matrix \(A\) has eigenvalues \(2\) and \(3\), what are the eigenvalues of the matrix \(A^2\)?
Which property of an estimator is satisfied if its expected value equals the population parameter?
For a Poisson distribution where the mean is \(4\), what is the value of the third central moment?
If \( P(A) = 0.4 \), \( P(B) = 0.5 \), and \(A\) and \(B\) are independent events, what is the value of \( P(A \cup B) \)?
Write the important assumptions of ANOVA.
In bivariate data following results were obtained.
Mean value of X = 53, Mean value of Y = 27, byx = -1.5, bxy = 0.2. Find the regression equation of X on Y and Y on X.
Equations of two lines of regression are \( 2x - 5y + 33 = 0 \) and \( 3x - 9y - 108 = 0 \). Which one is the regression line of \( y \) on \( x \)?
A random sample of 100 is taken from a population. The mean and standard deviation are respectively 76 and 12. Obtain a 99% confidence interval for the mean of the population.
Find the derivative of \( y = x^6 + 48x^3 + 24x - 16 \) with respect to \( x \).
A random sample from a population is given below. 35, 45, 40, 42, 39, 55 and 63. Obtain the moment estimator of the population mean.
In a distribution exactly normal, 7% of the items are under 35 and 89% are under 63. Find the mean and standard deviation of the distribution.
X+2Y=5 and 2X+3Y=8. Find the Mean of X and Y.
The ratio of two independent chi-square variables is _______.
The time taken by a student to reach the school is an example of _______ variable.