SSC CGL Tier-2 14th September 2018 Statistics

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For the following questions answer them individually
SSC CGL Tier-2 14th September 2018 Statistics - Question 1

The prices (in ₹) of different yarns (per kg) in two consecutive years are as follows.

By simple aggregative method, the net price changes in % is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 2

The average working hours per month of the staff aged over 50 yearsin a factory were 160 and that of the staff aged under 50 years were 210. The mean working hour per month of all the staff was 200. The ratio of the numberofthe staff aged over50 to thatof the staff aged under 50 is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 5

For a random variable x , the central moments $$(\mu_i)$$ of all order exist. The square of $$(2j + 1)^{th}$$ moment $$(\mu^2_{2j+1})$$ is always:

SSC CGL Tier-2 14th September 2018 Statistics - Question 7

If the random sample of size n is drawn without replacement from finite population of size N , the correction factor for standard error of sample mean will be:

SSC CGL Tier-2 14th September 2018 Statistics - Question 9

Let $$\left\{X_i, i \geq 1\right\}$$ be independent and identically distributed random variables with  $$P(X_i = 1) = p = 1 - P(X_i = 0), S_n = \sum_{i=1}^n X_i$$. The distribution of $$S_n$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 11

For the given figures of production of a sugar factory, the estimate of the production for 1976 using straight line trend with origin at the year 1972 by the least squares method $$\left(\sum x = 0, \sum x^2 = 28, \sum xy = 56\right)$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 21

With reference to index numbers, which of the following statements is true?

SSC CGL Tier-2 14th September 2018 Statistics - Question 22

If a discrete random variable X follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20, the value of $$P(\mid X - 14 \mid < 5)$$ will be:

SSC CGL Tier-2 14th September 2018 Statistics - Question 23

Marshall-Edgeworth Index number:

SSC CGL Tier-2 14th September 2018 Statistics - Question 24

The curve obtained by joining the points, whose x-coordinates are the upper limits of the class interval and y-coordinates are corresponding cumulativefrequencies is called:

SSC CGL Tier-2 14th September 2018 Statistics - Question 25

The probability density function of a random variable X is $$f(x) = \frac{\pi}{10} \sin \frac{\pi x}{5}; 0 \leq x \leq 5$$. The first quartile of X is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 26

60% of the employees of a companyare college graduates. Of these, 10% are in sales. Of the employees who did not graduate from college, 80% are in sales. The probability that an employee selected at randomisin sales, is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 27

By the method of moving averages, the seasonal index for four quarters equals to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 29

If the multiple correlation coefficient of $$X_1$$, on $$X_2$$, and $$X_3$$ is zero, then:

SSC CGL Tier-2 14th September 2018 Statistics - Question 30

The null hypothesis in ANOVA one-way classification, the study of the variances due to k different sources, is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 33

The probability of getting 9 cards of the samesuit in one hand at a game of bridge is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 35

A, B, and C are three mutually exclusive and exhaustive events associated with a random experiment. If $$P(B) = \frac{3}{2}P(A)$$ and $$P(C) = \frac{1}{2}P(B)$$ then value of $$P(A)$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 37

Following two statements are related to regression coefficient
(1) Independentof the changeoforigin
(II) Independentof the changeofscale

SSC CGL Tier-2 14th September 2018 Statistics - Question 39

If X has Binomial distribution with parameters $$n$$ and $$p$$ such that $$np = \lambda$$ then $$\lim_{n \rightarrow \propto}b(x, n, p);x = 0, 1, 2, ....$$ is equal to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 40

The given table shows ANOVA two-way classification to test two types of cloths in fashion trends.

The respective values (correct to two decimal places) of $$(\alpha, \beta, \gamma)$$ are:

SSC CGL Tier-2 14th September 2018 Statistics - Question 42

The approximate median of the Poissondistribution with parameter $$\lambda$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 43

If $$X_1, X_2, ...... X_n$$ is a simple random sample without replacement of size n from a finite population of N units with mean $$\mu$$ and $$\sigma^2$$, the covariance of $$(X_i, X_j)$$ will be:

SSC CGL Tier-2 14th September 2018 Statistics - Question 44

Which of the following approaches does multiplicative model have for the component of Time series Secular trend (T) , Seasonal variation (S) , Cyclical fluctuation (C) and Irregular movement(I) ?

SSC CGL Tier-2 14th September 2018 Statistics - Question 47

Let MSA defines mean sum of squares due to factor A and MSE defines mean sum of squares dueto error. If the null hypothesis of ANOVA for one way classification is not true, then $$\frac{E(MSA)}{E(MSE)}$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 49

If $$Z_1, Z_2, ..., Z_n$$ are $$n$$ independent standard normal variates, then $$\sum_{i=1}^n Z^2_i$$ will follow:

SSC CGL Tier-2 14th September 2018 Statistics - Question 50

The coefficient of correlation is r between X and Y having standard deviation $$\sigma_x$$ and $$\sigma_y$$ . The tangent of the angle

between two lines of regression is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 54

Let $$M, M_d, M_o$$ denote mean, median and mode and $$Q_1, Q_2$$ and $$Q_3$$ quartile points. Which of the following is an absolute measure of skewness?

SSC CGL Tier-2 14th September 2018 Statistics - Question 56

With reference to analysis of variance, which of the following statements is/are correct?
(I) Change of origin will affect the value of F .
(II) Change of scale will affect the value of F .

SSC CGL Tier-2 14th September 2018 Statistics - Question 59

The product of partial regression coefficient $$b_{12.3} b_{23.1} b_{31.2}$$ equals to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 66

If $$p(x) = \begin{cases}{\frac{x}{15};} & x = {1, 2, 3, 4, 5}\\0;& elsewhere\end{cases}$$, the probability $$P\left\{\frac{1}{2} < X < \frac{5}{2}\right\}$$ is equal to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 69

A dice was thrown 400 times and ‘six’ resulted 80 times. The data is used to justify the hypothesis of an unbiased dice at 95% confidence. With reference to the given case, which of the following statements is correct?

SSC CGL Tier-2 14th September 2018 Statistics - Question 70

The sample sizes for two cases were 15 each with means as 104 and 114 respectively and variances as 290 and 510 respectively. Let the null hypothesis is that the two population means are equal, then the value of t-statistic is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 72

If $$n_1 = 10$$ and $$n_2 = 5$$, are the sizes, $$\overline{x}_1, = 7$$ and $$\overline{x}_2, = 4$$ are the means and $$\sigma_1 = 1$$ and $$\sigma_2 = 1$$ are the standard deviations of two series of data. If combined mean $$\overline{x}_2, = 6$$, then the variance of the combined series with size $$n_1 + n_2$$ is equal to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 82

The problem of statistics is given in two sections of same standard. The odds against for section X to solve the problem are 4 : 3 and odds in favour to section Y for solving the same problem are 7 : 8. The probability that neither section solves the problem of statistics. if both sections try independent of each other, is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 84

$$\mu'_{(r)}$$ and $$\mu'_r$$ represent the factorial moment of order r about the origin and $$r^{th}$$ moment about the origin of the distribution $$x_i \mid f_i,i = 1,2,...n$$. The value of $$\mu'_2$$ equals to:

SSC CGL Tier-2 14th September 2018 Statistics - Question 86

If the independent random variables X,Y are Binomially distributed with $$n = 3, p = \frac{1}{3}$$ and $$n = 5, p = \frac{1}{3}$$ respectively, then the probability of $$(X + Y \geq 1)$$ is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 89

The square of normal variate with mean 0 and variance 1 follows:

SSC CGL Tier-2 14th September 2018 Statistics - Question 94

If the occurrence of events follows Poisson Process with mean rate $$\lambda$$ , then inter-occurrence time of events will follow:

SSC CGL Tier-2 14th September 2018 Statistics - Question 95

A random sample of 100 ball bearings selected from a shipment of 2000 ball bearing has an average diameter of 0.354 inches with standard deviation 0.048 inches. The 95% confidence interval for the average diameter of these 2000 ball bearings is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 97

In Spearman rank correlation coefficient $$r_s = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}$$, the maximum value of $$\sum d^2$$ in case of untied ranks is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 98

If $$x = X - \overline{X}$$ and $$y = Y - \overline{Y}$$ and the number of pairs $$(X,Y)$$ is n, then the Karl Pearson’s coefficient of correlation is:

SSC CGL Tier-2 14th September 2018 Statistics - Question 99

For a group of 100 students, the mean andstandard deviation of scores were found to be 30 and 5 respectively. Later on it was discovered that the scores 34 and 53 were misread as 43 and 35 respectively. The corrected mean equals to:

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