SAHIWAL BOARD 2016
PAPER STATISTICS
Note: Four Answers are given against each column A,B,C&D. Select the write answer and only separet answer sheet, fill the circle A,B,Cor D with pen or marker in front of that question number.
(a)![]()
(b)![]()
(c)![]()
(d)![]()
(a) -∞
(b) -1
(c) +1
(d) ∞
(a) 20
(b) 16
(c) 216
(d) 18
(a) Survey
(b) Pilot survey
(c) Census
(d) None
(a) 0.32σ
(b) 0.7979 σ
(c)σ
(d) 0.6745 σ
(a) Sample design
(b) Sampled population
(c) Sampling frame
(d) Target population
(a) CPU
(b) Program
(c) Language
(d) Input
(a) Regular
(b) Irregular
(c) Simple
(d) Upward
(a) Maximum
(b) Minimum
(c) Positive
(d) Negative
(a) Independent
(b) Associated
(c) Does not exist
(d) None
(a) α
(b) β
(c) (r-1)(c-1)
(d) None
(a) Regression
(b) Correlation
(c) Causation
(d) None
(a) var (x) = 0
(b) var (y)= 0
(c) cov (x, y) = 0
(d) None
(a) Intercept
(b) Slope
(c) Random error
(d) None
(a) α
(b) 1 - α
(c) β
(d) 1- β
(a) S2
(b) s2
(c) ρ
(d) None
(a) 0
(b) 1
(c) µ
(d) None
Time: 2;40 Hours:
(Subjective Part)
Marks: .68
SECTION-I
2. Write short answers of any Eight Parts.16
3.Write short answers of any Eight Parts:16
4.Write short answers of any Six Parts.12
SECTION II
Attempt any THREE Questions. Each Question carries 8 marks.
5.(a) In a normal distribution M.D = 3.9895, then find quartile deviation, standard deviation, second and fourth moment about mean of the normal distribution.
(b) If X ̴ N (µ,σ2), p (x < 40) = 0.1587 and p (x > 70) = 0.0228. Find µ and σ.
6.(a) A population consists of 2, 4, 6, 8, 10 values. Take all possible samples of size n = 2 without replacement and find samples mean. Show that E ()= µ , var (
) =
2.
(b) Two random sample each size 2 are taken with replacement from two population given as population II, 2 and 4, population II 2, and 3. From a sampling distribution of
(-
) and show that µ
-
= µ1 - µ2.
7(a) A random sample of 500 workers of the labour force in a certain region showed that 40 are unemployed. Construct the 95% confidence interval for the unemployed people in the region.
(b) Given the following information:
n = 30, = 15.2 , σ = 4 . Test the hypothesis that µ =15.0 at α= 0.05
8.(a) Fit a regression line Y = a + bx to the given data and show that Ʃ y = Ʃ ŷ.
X |
0 |
1 |
2 |
3 |
4 |
5 |
Y |
2 |
4.5 |
5 |
6.5 |
8 |
9 |
(b) Allot ranks to the given data, then find coefficient of rank correlation.
Supply |
440 |
225 |
710 |
95 |
515 |
330 |
575 |
Demand |
55 |
66 |
22 |
77 |
44 |
33 |
11 |
9.(a) In an investigation into eye-color and left or right handedness of a person, the following results were obtained:
Handedness |
||
Eye color |
Left |
Right |
Brown |
20 |
80 |
Blue |
15 |
85 |
Do these results indicate, at 5% level of significance, an association between eye-color and left or right handedness.
(b)Compute 4 - months centred moving averages from the following.
Moth |
Jan |
Feb |
Mar |
April |
May |
June |
July |
Aug |
Sep |
Oct |
Nov |
Values |
23 |
27 |
29 |
30 |
31 |
35 |
37 |
32 |
35 |
41 |
28 |
SECTION-III (Practica1.Parrt)
Note: Attempt any THREE questions.
10.(A)Take all possible samples of size 3 with replacement from a population:
1, 2. Make a sampling distribution of mean and show that α =
2 .
(B) Take all possible samples of size 3 with replacement from population: 1, 2. Show that sample mean () is an unbiased estimator of population mean (it) .
Given the following data:
Score |
480 |
490 |
510 |
530 |
550 |
GPA |
2.7 |
2.9 |
3.3 |
3.4 |
3.5 |
(C)Estimate regression line of GPA on score. Estimate the mean G.P.A of students scoring 580 marks.
(D) Given the data (AB) 110, (αβ) = 90,(A β) = 290,(αβ)= 510. Make a contingency table and find whether the two attributes are independent or associated. If they are associated, find whether association is negative or positive. Also find magnitude of association using some appropriate coefficient.
(E) Give The data
Year |
1973 |
1974 |
1975 |
1976 |
1977 |
(Y) |
201 |
238 |
392 |
507 |
649 |
Find trend values by semi average method. Also plot observed and trend values on the same graph.