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(12th CLASS - 12012)
STATISTICS
TIME: 20 MINUTES
MARKS: 17
OBJECTIVE

NOTE: You have four choices for each objective type question as A, B, C and D The choice which you think is correct fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank. Write the letter A, B, C or D in the column (Write correct option) against each question. If there is a contraction in the bubble and hand written answer bubble option be considered correct

QUESTION NO. 1

The maximum ordinate of the normal curve occurs at

(A) x = 0
(B) x = 5
(C) x = µ
(D) x = 1

The middle area under the normal curve with u ± 25 is

(A) 0.6827
(B) 1.0000
(C) 0.9545
(D) 0.9973

The normal distribution will be less spread out when

(A) The mean is small
(B) The median is small
(C) The mode is small
(D) The standard deviation is small

A sampling distribution might be based on which of the following

(A) sample means
(B) Sample proportions
(C) sample variances
(D) all of these

Difference between size is called

(A) Sampling error
(B) non sampling error
(C) simple error
(D) sample error

The expected value of — 2 is always equal to

(A) zero
(B) µ
(C) 5
(D) µ1 - µ2

Rejection of the null hypothesis when it is infect true is a

(A) Type I error
(B) Type II error
(C) B error
(D) correct decision

In using a one sample t-test which of the following statements is true

(A) 5 must be known
(B) population must be normal
(C) n must he large
(D) d.f≥n

The value of β gives the

(A) power of test
(B) P(Type I error)
(C) P(type II error)
(D) Confidence level

In the context of regression , the dependent variable is also called

(A) regressand
(B) regressor
(C) predictor
(D) y — intercept

For a given set of bivariate data if byx = - 0.52 and bxy = - 1.02 , then ‘r’ is

(A) 0.73
(B) – 0.73
(C) 0.00
(D) 1.00

For a given set of bivariate data , if byx = bxy ‘r’ , then

(A) Sx ≠ Sy
(B) Sx > Sy ,
(C) Sx < Sy
(D) Sx = Sy

If (A8) < (A)(B/N then the association) then the association is

(A) Positive
(B) Negative
(C) Perfect
(D) None of these

Yates correction for continuity is applied is

(A) All cases
(B) A 2 x 2 contingency table
(C) A 3 x 3 contingency table
(D) None of these

For a least squares linear trend + bx , then ∑(y — )2 = 0 when

(A) All the y — values lie on the line
(B) All the y —values are positive
(C) All the y — values lie above the line
(D) None of these

Shortage of certain consumer goods before annual budget is

(A) Seasonal variation
(B) cyclical variation
(C) Secular trend
(D) Irregular variation

A binary digit is commonly called

(A) byte
(B) kilobyte
(C) gigabyte
(D) bit

STATISTICS
(12th CLASS - 12E1)
HME: 1.40 HOURS
SUBJECTIVE
MARKS 68
SECTION

QUESTION NO. 2 Write short answers of my eight questions of the following 16

If X is N(25, 25) Find the value is of maximum ordinate
If ZN (0 , 1) verify that P( z<2.5) = P( z ˃-2.5)
In a normal distribution the lower and upper quartiles are 20 and 40 respectively, Find µ
If X is N(50 ,100). Find P(x < u)
What is meant by estimation?
Distinguish between null hypothesis and alternative hypothesis
Define the power of test
Explain type-I error with one example
Differentiate between point_ estimate and interval estimate
Differentiate between analog computers and digital, computers
Differentiate between floppy disk and compact disk

QUESTION NO. 3 Write short answers of my eight questions of following 16

Differentiate between finite an l infinite population
Define sampling, error
Give four uses of sampling
Define with replacement sampling
Differentiate between statistic and parameter
If 62 =10, N= 10 n= 4 Find
What is meant by regression?
Define simple linear regression
Write down the two properties regression coefficient
If = 0.6x + 2, and = 0.4 y...3 Find ϒ
Define perfect negative correlation
Write the relation between regression coefficient and correlation coefficient

QUESTION NO. 4 Write short answers of any six questions of the following 12

Define Historigram
Differentiate between signal and Noise
Explain the seasonal variation with example
What do you meant by the analysis of time series
Define Irregular variation
Name the Method measuring, the secular trend
Define Positive and Negative association
Define the contingency table
Define Attribut

SECTION-II

Note: Attempt any Three questions from this section 8 x 3=24

5.
(a) The scores made by candidates in a certain test are normally distributed with mean 500 and standard deviation 125. What percentage Of Cardidates received scores ?                          4
(i) More than 700
(ii) Less than 400
(iii) Between 375 to 625

(b) Two quartiles of normal distribution are 9 and 18    4
Required :
(i)   µ
(ii) ϭ
(iii) M.D

6,
(a) A population consists of 6 values 1, 3 , 5 , 7 , 9 ,11 . Take all possible samples of size 2 which can be drawn without replacement. Find mean and variance of the sampling distribution of means. Also verify the results. 4

(b) If mean and variance of population an 7 and 3.15 respectively what would be the standard error of mean if samples are drawn without replacement of size 6 from a population of site 10 4

7,
(a) Two samples of sizes (n1 = 45, n2 = 6 ) respectively are taken from a population with unknown /> mean (u) and variance (ϭ2) . By the use of the following informations, find the best estimate of µ and ϭ2
Sample 1 :        ∑fx1= 847             ∑fx21 = 17410
Sample II    :         ∑fx2 =1060 ,        ∑fx22 =   104

(b)    If = 0.30 , = 0.25, n1 =1200, n2 = 900 α = 0.05 Find value of Z and make the statistical decision by some suitable procedure for Ho : p1 = p2 against H1: p1 ≠ p2

8.
(i) Ditrr6ne the minuted regression equation =a a+bx
(i) =52    = 237       ∑(x —)=2800      ∑(x —) (y —)=9871
(ii) ∑xy=350                         n=10           =6 S2x=4          =9

(b)    Given the following results
x= 10      = 65     Sx 7- 23.23     ; =56   Sy = 14.0      ∑(x —) (y —)=1704
Show that          = b x b4 x