Statistics Sindh CCE Paper 2023

SINDH PUBLIC SERVICE COMMISSION, HYDERABAD

COMBINED COMPETITIVE EXAMINATION, 2023

STATISTICS

Tuesday 22^nd April, 2025
Time. 09:00 am to 12:00 Noon
Maximum Marks.100

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Note: Attempt any Five questions in all by selecting Three questions from Section-I and Two questions from Section-II.

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Question No.		Marks
SECTION-I
01 (A)	Define ‘Standard deviation’, why it is superior over the other measures of dispersion?	06
(B)	If the mean of 10 items is 45.5 and standard deviation is 2.8. It is later discovered that one observation 54 was wrongly entered to the computer, while the correct value was 44. Compute the correct mean and standard deviation.	14
02 (A)	Define the following terms: (i) Permutation and Combination (ii) Addition law of probability (iii) Probability and its Axioms	06
(B)	How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, and 7, if each digit can be used only once? How many of these are even numbers?	06
(C)	One box contains three black chips and two red chips. Another box contains two black and five red chips. First box is selected if the digit appears on die is even and a chip is drawn. If the digit is odd the chip is drawn from the second box. Find the probability that a black chip is drawn.	08
03 (A)	Define the Pearson’s correlation coefficient along with its properties.	06
(B)	The grades of a class of 8 students on a mid-term report (X) and on the final examination (Y) are as follows: X 77 50 71 72 81 94 96 99 Y 82 66 78 34 47 85 99 99 (i) Compute the coefficient of correlation for the data. (ii) Estimate the regression line Y on X (i.e. Y = α + βX + ε). (iii) Estimate the value of Y for each given value of X. (iv) Find the error e = Y – Ŷ	14
04 (A)	Distinguish between (i) Classical or a priori probability, (ii) Relative frequency or a posteriori probability and (iii) Subjective probability. What are the advantages in each case?	05
(B)	A certain event is believed to follow the binomial distribution. In N = 1024 samples of n = 5, the result was observed once 405 times and twice 270 times. Find p and q?	05
(C)	The frequency of accidents per shift in a factory is shown in the following table. Use the Poisson distribution to estimate the probability of (i) no accident in a shift, and (ii) more than one accident in a shift. Accidents per shift 0 1 2 3 4 5 Frequency 300 96 34 9 1 0	10

SECTION-II

05 (A) Define the term ‘Sample Survey’. What are the principle steps in conducting a sample survey? Briefly describe them. 06 (B) Define “Stratified random sampling”. Give the real-life situations in which this sampling is useful instead of using the method of Simple random sampling or/and cluster sampling. 06 (C) A random sample of 1000 registered voters from the state of Illinois are classified as to whether they are in a low, medium or high-income bracket and whether or not they favour a new tax reform. The observed frequencies are presented in the table given below:

Tax Reform	Income Level			Total
	Low	Medium	High
For	182	213	203	598
Against	154	138	110	402
Total	336	351	313	1000

Can we conclude from these data at 0.05 level of significance that the income level of voters is independent of their opinion about the new tax reform? 08

06 (A) Define the vital statistics with its applications. Distinguish between the following:
(i) Rates and Ratios
(ii) Birth rates and Death rates
(iii) Crude rates and specific rates 10 (B) Define the term ‘Official Statistics’ along with its importance. Give two main sources of official statistics in Pakistan. 10

07 (A) Differentiate between:
(i) Null and alternative hypothesis
(ii) Simple and composite hypothesis
(iii) Acceptance and rejection regions
(iv) Type I and Type II errors and (v) One tailed and two tailed tests. 10 (B) A basketball player hits 60% of his shots from the floor. If the next 100 shots he makes 70 baskets, would you say that his shooting has improved? Use α = 5% level of significance. 05 (C) A random sample of size 100 from a normal population shows a standard deviation of 8.9. Test at α = 5% level of significance by setting the hypothesis that σ = 7.5 against the alternative that σ ≠ 7.5. 05

08 Write short notes on the following:
(i) Completely randomized design
(ii) Total fertility and net-reproduction rates.
(iii) Statistical system for data collection in Pakistan.
(iv) Role of Pakistan Bureau of Statistics. 20