CSS 2025 Statistics Past Paper

Paper details

Examination

CSS

Year

2025

Subject

Statistics

Paper

Single Paper

Subject type

Optional

Mode

Subjective

Questions recorded from this paper

These 7 question wordings are transcribed from CSS Vista’s structured Statistics past-paper record for CSS 2025.

1. Q4 · Properties(a) If X has a binomial distribution, then show that E(X) = np, Var(X) = npq. Derive the (10) m.g.f of the binomial distribution and explain its uses? (b) What are the main characteristics of the Poisson distribution? Explain with the help of (10) (20) examples. Also give its properties, applications and relationship with other distributions.
2. Q5 · Properties of Correlation Coefficient(a) From the following set of values: (10) Y 6.5 5.3 8.6 1.2 4.2 2.9 1.1 3.0 X 3.2 2.7 4.5 1.0 2.0 1.7 0.6 1.9 1) Compute the residuals and verify that they add to zero and draw the conclusion about the results. 2) Compute the standard error of estimate, sy.x. (b) Under what conditions the correlation among the random variables exists. Also describe (10) (20) the properties of correlation coefficient. Calculate the correlation co-efficient for a sample of 20 pairs of observations, given that Mean of X = 2, Mean of Y = 8, ∑ X 2 = 180, ∑ Y 2 = 1424 and ∑ XY = 404 Also interpret its results.
3. Q2 · Sampling Distribution of Mean(a) What is the purpose of frequency distribution and what are its desirable qualities? For a (10) certain frequency distribution, the mean was 40.5 and the median 36. Find the mode approximately using the formula connecting the three. (b) Define Statistics. Discuss the importance of study of statistics by giving examples. How (10) (20) it can help the extension of scientific knowledge?
4. Q3 · Sampling Distribution of Mean(a) Explain what is meant by the skewness of the distribution, and define a suitable measure (10) of Skewness. For given p.d.f. f (x) = k (x – x2), 0≤x≤1 Find the Skewness and discuss. (b) Define the normal distribution and obtain its mean and variance. Show that for the (10) (20) normal distribution, the mean, mode and median are the same.
5. Q6 · Sampling Distribution of Mean(a) What is finite-correction factor? When is it appropriately used in sampling applications (10) and when can it, without the great undesirable consequences, be ignored? (b) Given the population 2, 4, 8, 8, 10, 10. (10) (20) 1) How many samples of size n = 2 can be drawn without replacement from this population? 2) Compute and tabulate the sampling distribution of the mean for samples of size n = 2.
6. Q7 · Hypothesis Testing: Types of errors(a) Explain what is meant by: (10) (i) a statistical hypothesis, (ii) test-statistic, (iii) test of significance, (iv) level of significance, (v) type-I error and type-II error (b) The weights of 4 persons before they stopped smoking and 5 weeks after they stopped (10) (20) smoking are as follows: Person 1 2 3 4 Before 148 176 153 116 After 154 176 151 121 Use the t-test for paired observations to test the hypothesis at the 0.05 level of significance, that giving up smoking has no effect on a person’s weight.
7. Q8 · Randomized Complete Block Design (RCBD)(a) Explain the procedure of randomization in a completely randomized design where we (10) have 3 varieties of wheat and 18 experimental plots available. Also explain what is explained by significant F value in an experiment. (b) Four varieties of wheat were tried in a randomized complete block design in four (10) (20) replications. Yield in kilogram per plot is shown in the table given below. Test the hypothesis that there is no difference in the means of four varieties. α = 0.05. Replicates Varieties

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