SSC CGL Tier 2 28th January 2022 Statistics

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SSC CGL Tier 2 28th January 2022 Statistics - Question 2

Rohit wants to check his IQ with an MCQ test. The test has five questions with one correct answer. Each question has three options. If he just randomly guesses the answer to each question, what is the probability that he will get exactly three questions correct?

SSC CGL Tier 2 28th January 2022 Statistics - Question 3

For the uniformly distributed random variable X with a = 0 and b = $$\theta$$, the value of the ratio of raw moments $$\left(\frac{\mu_{3}}{\mu_{4}}\right)$$ is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 4

If $$n_{1} = 10,n_{2} = 5$$ are the sizes of a male and female student group with mean ages $$\overline{x_{1}} = 10, \overline{x_{2}} = 4$$, respectively, with an equal standard deviation $$\sigma_{1} = 1, = \sigma_ 2$$ the standard deviation of the combined series with size $$n_{1} + n_{2} $$, and combined mean $$\overline{x} = 8$$ is equal to:

SSC CGL Tier 2 28th January 2022 Statistics - Question 6

The average income of a worker for the first five days of the week is ₹25 per day. If he works for the first six days of the week, his average income per day is ₹30. His income for the sixth day is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 10

Multiple regression equation of $$X_{1}$$ on $$X_{2}$$ and $$X_{3}$$ is $$\left(X_{1} -\overline{X}_{1}\right) = b_{12.3}\left(X_{2} -\overline{X}_{2}\right) + b_{13.2}\left(X_{3} -\overline{X}_{3}\right)$$ where $$ b_{13.2}$$ is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 11

The prices (in ₹) of vegetables (per 5 kg) in the years 2019 and 2020 are as follows:
2019: 60 (Potato); 70 (Onion); 40 (Tomato); 30 (Chilli)
2020: 70 (Potato); 60 (Onion); 48 (Tomato); 27 (Chilli)
By the simple aggregative method, the net price changes in percentage are:

SSC CGL Tier 2 28th January 2022 Statistics - Question 23

A sample of 30 latest, returns on UTI stock with unknown standard deviation reveals a mean return of $4. The estimated standard error of the sample means is 0.02. How much more of the sample (approximately) should be added to reduce the standard error of the sample mean to 0.01?

SSC CGL Tier 2 28th January 2022 Statistics - Question 24

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

SSC CGL Tier 2 28th January 2022 Statistics - Question 25

The coefficient of mean deviation about median equals to:

SSC CGL Tier 2 28th January 2022 Statistics - Question 27

The lower quartile of $$f\left(x\right) = \frac{1}{12}\left(5-2x\right); -1 \leq x \leq 2$$ is one root of the quadratic equation:

SSC CGL Tier 2 28th January 2022 Statistics - Question 29

The following measures were computed for a non-symmetrical frequency distribution: mean = 50, coefficient of variation = 35% and Karl Pearson's coefficient of skewness of first type= -0.25. The value of mode of the distribution is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 33

Boy child is more probable than girl child to a couple in 2019. A random sample found 224 boys were born among 400 newborn children. For this sample evidence that the birth of boys is more common than the birth of girls in the entire couple population, the value of test statistics is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 34

We measure ten units from the latest production lot to measure the length of the product that gives the sample mean to be 17.55 inches, and the sample standard deviation to be 1.0 inch. The 95%, confidence interval for the population mean is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 37

In averaging the price relatives, which of the following options is the most appropriate average?

SSC CGL Tier 2 28th January 2022 Statistics - Question 40

The median of a Weibull distribution with shape parameter k and scale parameter $$\lambda$$ is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 43

If X follows the normal distribution with mean $$\mu$$ and variance $$\sigma^{2}$$, the fourth moment about origin is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 44

The television habits of 30 children were observed. The sample mean was found to be 8.2 hours per day, with a standard deviation of 2.4 hours per day. You tested the claim that the standard deviation was at least 6 hours per day. The value of the test statistics is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 47

The ANOVA was used to test the results of three drug treatments. Each drug was applied to 20 patients. The MSE for this study was 16. What is the estimate of the population standard deviation for all 60 patients sampled for this study?

SSC CGL Tier 2 28th January 2022 Statistics - Question 51

A number is selected randomly from each of the given two sets.
Set 1: 1 , 2, 3, 4, 5, 7, 8
Set 2: 2, 3, 4, 5, 6, 7, 8, 9
The probability that the sum of the numbers is equal to 9 is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 52

Let there be no overlap between the box and whisker plots for three drug treatments where each drug was administered to 35 individuals. The box plots for this data:

SSC CGL Tier 2 28th January 2022 Statistics - Question 56

In a library, there are 40% mathematics books and the remaining 60% are science books. It is known that 2% of the mathematics books are in Hindi, and 1% of the science books are in Hindi. If one book is taken out at random and is found to be in Hindi, the probability that it is a science book is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 57

If $$A_{1}, A_{2}, A_{3}$$ are three mutually exclusive events, the probability of their union is equal to:

SSC CGL Tier 2 28th January 2022 Statistics - Question 58

Which of the following options is correct?

SSC CGL Tier 2 28th January 2022 Statistics - Question 59

Suppose that the CDF of X is given by $$f\left(x\right) = \begin{cases}0;x < 0 &\\\frac{1}{5};0\leq x <2 & \\\frac{2}{5};2\leq x <4 \\ 1; x \geq4 \end{cases}$$
The value of P(X = 4) is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 62

For the data on early earning of employees in a company, the raw moments about some arbitrary poim A = 12 is given by $$\mu_{1} = -3, \mu_{1} =94, \mu_{3} = 546, \mu_{3} = 2200$$. The moment $$\mu_{3}$$ about actual mean 94 is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 65

Let X and Y be independent random variables that denote the number of virus 1 and virus 2, respectively, in one room, follow Poisson distribution with parameter $$\lambda_{1} = 1 $$ and $$\lambda_{2} = 2 $$ respectively. The expected number of viruses in the room is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 71

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

SSC CGL Tier 2 28th January 2022 Statistics - Question 72

If X is a random variable with PDF $$f\left(x\right) = \frac{x^{2}}{9}; 0 < x < 3$$ the cumulative contribution function of $$Y = X^{5}$$

SSC CGL Tier 2 28th January 2022 Statistics - Question 74

The change in the prices and quantities of each individual commodity are summarised as follows:

The Laspeyres Price Index for the year 2017. using the year 2016 as the base year, is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 76

In the absence of skewness, the coefficient of skewness by Karl Pearson $$\left(S_{k}\right)$$, Bowley's $$\left(S_{q}\right)$$ and by Kelly's $$\left(S_{p}\right)$$ are:

SSC CGL Tier 2 28th January 2022 Statistics - Question 77

If X and Y are two random variables such that their expectations exist and $$P(X \leq Y) = 1$$, then which of the following opctons is true?

SSC CGL Tier 2 28th January 2022 Statistics - Question 82

For the joint density $$f_{xy}\left(xy\right) = x + \frac{3}{2}y^{2};0\leq x \leq 1,0 \leq y \leq 1$$, the value of $$P\left(0 \leq Y \leq \frac{1}{2}\mid 0 \leq X \leq \frac{1}{2}\right)$$ is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 83

In the completely randomised design, the variance between columns depicts the difference between the ___ of each group and the ___

SSC CGL Tier 2 28th January 2022 Statistics - Question 86

Given that $$P\left(A\right) = 1/3, P\left(B\right) = 1/4, P\left(A\mid B\right) = 1/6$$, the probability $$ P\left(B\mid A\right)$$ is equal to:

SSC CGL Tier 2 28th January 2022 Statistics - Question 88

If the Bowley's coefficient of skewness $$S_{q}$$ is positive, which of the following options is correct?

SSC CGL Tier 2 28th January 2022 Statistics - Question 89

The first four raw moments of distribution are 2, 136, 320 and 40.000. The coefficient of kurtosis is:

SSC CGL Tier 2 28th January 2022 Statistics - Question 91

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

SSC CGL Tier 2 28th January 2022 Statistics - Question 93

The workers at a large manufacturing company can earn monthly bonuses. The distribution of monthly bonuses earned by all workers last year has a mean of 2.3 and a standard deviation 1.3. Let Z represent the standard normal distribution. If X represents the mean of monthly bonuses earned last year for a random sample of 40 workers. which of the following gives the approximate probability that X is less than 2?

SSC CGL Tier 2 28th January 2022 Statistics - Question 97

What two pieces of information are needed at given level of significance for the determination of the critical value for testing whether the test statistic of ANOVA is statistically significant?

SSC CGL Tier 2 28th January 2022 Statistics - Question 99

The profit of a company during the first five months of a year is ₹Ninety-six lakhs per month and during the last seven months is ₹120 lakhs per month. The average profit per month during the whole year is:

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