List of top Statistical Science Questions on Statistics

If the regression coefficient of X on Y is \(b_{xy}\), and the variables are transformed as \(U = \frac{X - a}{h}\), \(V = \frac{Y - b}{k}\), then the regression coefficient of U on V is:

If regression line of X on Y is linear, then the regression line of Y on X is:

In case of Simple Random Sampling with Replacement, the sample mean:

The sum of absolute deviations is minimum when taken from:

The range of Coefficient of Variation (CV) is:

The minimum number of blocks required for 6 treatments so that the error degrees of freedom is 10 in case of a randomized complete block design is:

The Fairfield Smith's Variance law used in uniformity trials to obtain the relationship between plot size and plot variance is of the form \((V_x\) is the variance of yield per unit area from plots of size \(x\), \(V_1\) is the variance among plots of size unity and \(b\) is the coefficient representing soil characteristic):

Let the Arithmetic Mean of \(n\) observations be AM. If 5 is added to all the observations, then the new AM will be:

The sum of the deviations of the observations 3, 4, 5, 6, 7 from their mean is:

Let \(x_1, x_2, \dots, x_n\) be observations which have a variance \(\sigma_x^2\). Each \(x_i\) is changed to \(a x_i - h\), where \(a\) and \(h\) are positive constants, then the new series will have variance:

Mean, mode and variance of a given dataset are 60, 76 and 16, respectively. The value of Coefficient of Skewness of the dataset is:

If each value of variable X is multiplied by 8 and of Y is multiplied by 10, then correlation coefficient of new data is:

It is given that the standard deviation of a large population is 10. To test \(H_0: \mu = 10\) against \(H_1: \mu \neq 10\) at \(1\%\) level of significance, a sample of size 100 is taken. \(H_0\) will be rejected if:

There are 15 students in a class. Out of these 6 students failed. The marks of the passed students are 51, 67, 48, 71, 46, 45, 81, 90 and 50. The median of all the observations is:

Which of the following is NOT true?

In a completely randomized design with 5 treatments, treatments 1 and 2 are replicated 4 times each and treatments 3, 4 and 5 are replicated 3 times each. The degrees of freedom for error will be:

The principle of replication:

In normal distribution with mean \(\mu\) and variance \(\sigma^2\), the area under the normal curve between \(\mu \pm \sigma\) is:

Let X be a normally distributed random variable with mean \(\mu = 50\) and variance \(\sigma^2 = 9\). The probability that X is greater than \(\mu + \sigma\) is:

Which of the following is a simple hypothesis?

Which of the following statements is correct?

For testing goodness of fit, suppose the observed frequencies for two classes are 28 and 12. It is expected that these occur in the ratio 3:1. The value of Chi-square statistic for testing this is:

In a random sample of 100 voters in an area, 59 voters were in favour of a candidate A. The value of the test statistic for testing \(H_0: P = 0.5\) against \(H_0: P \neq 0.5\) is:

The coefficient of variation of Poisson distribution with mean 9 is: