List of top Statistical Science Questions

If all frequencies of classes are same, the value of chi-square ($\chi^2$) is:

Let X be a random variable with p.d.f. f(x) =6x(1-x), 0\(\le\) x \(\le\)1. Determine the value of b such that P(X < b)=P(X > b).
1. \(\frac{1}{2}\)
2. \(\frac{1 \mp \sqrt{3}}{2}\)
3. 0
4. \(\frac{1}{3}\)

If X and Y are independent Poisson variates, What is the distribution of \(\frac{X}{X+Y}\)?
1. Binomial distribution
2. Poisson distribution
3. Negative binomial distribution
4. Multinomial distribution

The range of Correlation coefficient is
1. -1 to +1
2. -1 to 0
3. 0 to +1
4. -\(\infty\) to +\(\infty\)

The relationship between root mean square deviation (r.m.s.d.) and standard deviation (s.d.) is
1. s.d. = highest value of r.m.s.d.
2. s.d. = least value of r.m.s.d.
3. s.d. = r.m.s.d.
4. s.d. = (r.m.s.d)/2

A person speaks truth 4 out of 5 times. A die is tossed. He reports that there is a six. What is the chance that actually there was six?
1. \(\frac{4}{9}\)
2. \(\frac{5}{9}\)
3. \(\frac{1}{9}\)
4. \(\frac{1}{3}\)

For any discrete distribution, what is the value of $\beta_2$?

A random sample of size 20 from a normal population gives a mean 42 and variance 25. To test that the population standard deviation is 8, the value of test statistics is
1. 7.42
2. 15.62
3. 51.20
4. 55.60

In Simple Random Sampling with replacement (SRSWR), the total no. of samples (with standard notation) will be
1. \(\binom{N}{n}\)
2. \(N^n\)
3. n + N
4. n*N

Let random variables \(X_1, X_2, \dots, X_k\) follows a multinomial distribution with parameter n and \(p_i\) where i= 1, 2,...,k. what is the value of Cov(\(X_i, X_j\))?
1. \(np_ip_j\)
2. \(-np_ip_j\)
3. \(p_ip_j\)
4. \(-p_ip_j\)

Given the eight sample values as -4, -3, -3, 0, 3, 3, 4, 4, the value of student's t- test \(H_0: \mu=0\) is:
1. 2.73
2. 0.97
3. 3.30
4. 0.41

If two independent random variable X and Y are binomially distributed with \(n_1=4\), p=(1/3) and \(n_2=5\), p= (1/3) respectively, Find the mode of the distribution of (X+Y).
1. 3, 2
2. 3
3. 3, 4
4. 4

Suppose the correlation coefficient for a pair of 625 random sample is 0.2. Is the value of r significant? Given \(t_{0.05, 623} = 1.96\).
1. Yes, value of r is significant
2. No, value of r is not significant
3. may or may not be significant
4. test is invalid

A sample consists of:
1. All units of the population
2. 5% units of the population
3. 12.5% units of the population
4. Any fraction of the population

X and Y are two random variable with \(\mu_X = 18.4\), \(\mu_Y = 33\), \(\sigma_X = 8.4\), \(\sigma_Y = 6.4\) and \(\rho_{XY} = 0.84\). The regression line of Y on X is
1. Y = X + 7.3
2. Y = 0.64X+21.22
3. Y = 0.64X+10.61
4. Y = 0.4X+12.82

The relation between standard deviation (SD), mean deviation about mean (MD) and quartile deviation (QD) is
1. 4SD = 6MD = 5QD
2. 4SD = 5MD = 6QD
3. 6SD = 5MD = 4SD
4. 5SD = 4MD = 6QD

Let \(\bar{X}\) be the mean of a random variable of size 5 from a normal distribution with \(\mu=0\) and variance \(\sigma^2 = 125\). Determine c so that P(\(\bar{X} < c\)) = 0.90
1. 6.10
2. 6.20
3. 6.30
4. 6.40

In RCBD we may assume that the treatment are fixed and the blocks are random, such a model is called

If in the CRD some observations are missing then also the analysis is very simple, because the missing observations are discarded and we carry out the experiment without losing the......

In the standard normal distribution, P(Z $\le$ 0) is equal to:
1. 1
2. 0.5
3. >0
4. <1

If the regression line is given by $X = 2 + 4Y$, then the correlation coefficient ($r$) is

Chose the correct answer:
1. Measures of skewness are independent of origin and scale
2. Measures of skewness are independent of origin and not of scale
3. Measures of skewness are independent of scale and not of origin
4. Measures of skewness are dependent of origin and scale

A student while calculating the mean of 25 observations obtained a mean of 56 cm. It was later discovered at the time of checking that he had wrongly copied down an observation as 64. What is the mean if the correct value is omitted?

If 3% of calculators are defective, find the standard deviation of the defectives in 300 calculators?

“Salaries of the employees in ICAR”, is an example of which level of measurement?