Download B.Sc(Stat) Up to date Papers Sampling(2008-2014)

B.Sc(Stat) Up to date Papers Sampling(2008-2014)
1:-Theory:Q1:-
Define & explain briefly the following
i)
Sampling Unit
SRG-2010
ii)
Sampling Frame
iii)
Sampling Design
Q2:-
Distinguish between a parameter and statistic. What is meant by Standard error and what are its practical
use.
SRG-2010
Q3:-
Distinguish between the following:
(i)
(ii)
SRG-2008/A
Random Sampling & Simple Random Sampling (iii)
Multistage & Multistage Sampling.
Sampling & Non Sampling Error
Q4:-
State central limit theorem.
SRG-2008/A, SGR-2012
Q5:-
Distinguish between Stratified Random Sampling & Cluster Sampling.
SRG-2008/A
Q6:-
Describe in brief, the sampling distribution of difference between proportions and explain its properties.
SRG-2007/A
Q7:
-Distinguish between;
(i) Target and sampled population
SRG-2007/A
(ii)
Sampling with and without replacement.
Q8:-
Define probability and non probability sampling giving examples of each.
SRG-2011/A
Q9:-
Differentiate the following terms:
SRG-2011/A
(i) Sample distribution & Sampling distribution.
Q10:-
(ii)
Standard deviation & standard error.
what is meant by sampling? Describe the advantages of sampling over complete enumeration?
Q11:- Define & distinguish between. (i) Target & Sampled Population.
sampling
(iii) Sampling & Non Sampling Errors.
(ii)Probability
& non
SRG-2013
SRG-2014
Probability
Q12:- What is meant by the term sampling distribution of sample proportion P? Describe its important properties
and explain its usefulness in statistical inferences.
SRG-2013
2:-Sampling:Q1:-
Suppose a small town has a total of 350 households; select a sample of 15 households, using SRG-2010
i)
Random Number Table
ii)
Systematic Sampling Technique
Q2:-
Select a random sample of size 20 using random number table from a Poisson distribution with parameter µ=2
SRG-2010(Just like Q14.19 P-58)
3:-Sampling with Replacement
A:-Mean
a:-One Population & one sample
Q1:A population consisting of 1000 men has a height distribution with Ϭ=3. How large a sample should be taken
to obtain “0.424” as a value of standard error of sample mean, when the sample is done with replacement?
SRG-2008/A
Q2:The heights of 1000 students are approximately normally distributed with a mean of 68.5 inches and a
standard deviation of 2.7 inches. If 200 random samples of size 25 are drawn from this population and the means
recorded to the nearest tenth of an inch, determine.
SRG-2007/A
(i)
The expected mean and standard deviation of the sampling distribution of the mean.
(ii)
The number of sample means that fall between 67.9 and 69.2 inclusive.
Q3:-
If the size of a sample is 36 and standard error of the mean is 2, what must be the size of the sample becomes,
if the standard error is reduced to 1.2.
SRG-2011/A
Q4:-
A random sample of 100 is taken from a population with mean 30 and standard deviation 15. The distribution
of parent population is unknown.
SRG-2011/A
(i) What is the shape of the sampling distribution of means?
(ii)
Standard deviation and standard error.
Q5:-
The height of 1000 students are approximately normally distributed with a mean of 68.5 inches and a
standard deviation of 2.7 inches. If 200 random samples of size 25 are drawn from this population and the
means are recorded to the nearest tenth of an inch, determine (a) the expected mean and standard deviation
for the sampling distribution of the mean if sampling were done
(i)
with replacement and (ii)
without replacement.
SRG-2013
Q6:-
The number of samples means that fall between 67.9 and 69.2 inches inclusive.
SRG-2013
Q7:-
The number of sample means falling below 67.0 inches .
SRG-2013
Q8:-
Given the following population distribution.
SRG-2013
X
1
2
3
4
F(X)
1/7
3/7
2/7
1/7
Find the sampling distribution of the mean if a sample of three numbers is taken with replacement. How does the
variance of the sampling distribution compare with the population variance?
Q9:If a certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation
of 2 ohms. What is the probability that a random sample of 36 resistors will have a combined resistance of more than
1458 ohms?
SRG-2007/A
Q10:- The weights of 1500 ball bearings are normally distributed with a mean of 22.40 ounces and a standard
deviation of 0.048 ounces. If 300 random samples of size 36 are drawn from this population, (i) determine the
expected mean and standard deviation of the sampling distribution of mean if the sampling is done without
replacement. (ii) How many of the random samples would have their mean between 22.39 and 22.42 ounces? SRG-2014
b:-Two Population & two sample
Q1:A & B manufacture two types of cables having mean breaking strength of 4000 & 4500 pounds respectively
and a standard deviation of 300 & 200 pounds respectively. If 100 cables of each brands are used. What is the
probability that the mean breaking strength of B will be at least 600 pounds more than A.
SRG-2008/A
B:-Variance
Q1:A population consists of five observations 1, 2, 3, 4, 5. Draw all possible samples of size 2 with replacement.
Find the mean of sampling distribution of variance. Compare it with variance of the population.
SRG-2012
C:-Proportion
Q1:- Consider the population of letters “Lahore”. Draw all possible samples of size “2” without replacement and find
the proportion of vowel letters in each sample. State & verify the relation between
SRG-2008/A
(i) Mean of sample proportions & population Proportion. ii) Variance of sample proportions & population proportion.
4:-Sampling without Replacement
Q1:A small professional society has N=4500 members. The president has mailed n=400 questionnaires to a
random sample of members assigning whether they wish to affiliate with a larger group. Assuming that the
proportion of entire membership favoring the consolidation is P=0.7, find the probability that sample proportion p
differs from this by no more than 0.05.
SRG-2007/A
Q2:-
Consider the following population distribution.
X
1
2
3
4
5
f(x)
2/7
1/7
1/7
2/7
1/7
Draw all possible samples of size “3” without replacement from this population and find the sample proportion of
odd numbers in each sample.
(i) Up^=P
(ii)
𝒑𝒒 𝑵−𝒏
Ϭ2p^= 𝒏 (𝑵−𝟏)
B.Sc(Stat) Up to date Papers Estimation(2008-2014)
Q1:-
(a) Differentiate between point & interval estimate.
SRG-2012
(b) If x1, x2, …..xn are the values of a random sample of size n from poison population with parameter ƛ. Find the
estimate of ƛ 𝒖𝒔𝒊𝒏𝒈 𝒕𝒉𝒆 𝒎𝒆𝒕𝒉𝒐𝒅 𝒐𝒇 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 likehood.
SRG-2012
(c) A random sample of size n=144 gave P=0.76. Construct a 90% confidence interval for P and interpret the result.
SRG-2012
B.Sc(Stat)
Up to date Papers Testing of Hypothesis(2008-2014)
Theory
Q1:-
Distinguish between one tail & two tail test.
SRG-2010
Q2:-
What is meant by:(i) Power of a test(ii) Test of significance(iii)Level of confidence.
SRG-2008/A
Q3:-
Explain what is meant by:(i) Statistical Hypothesis(ii)Test Statistic(iii) Operating characteristic function. SRG-2010
Q4:-
How probabilities of committing type 1 & type II error are related? Are they additive?∝+β=1. SRG-2008/A
Q5:-
Differentiate the following terms:
SRG-2011/A
(i) Hypothesis and Statistical hypothesis. (ii)
Q6:-
One tail & two tail test. (iii) Level of significance & confidence.
(a) Explain with examples the difference between (i) Null Hypothesis & Alternative Hypothesis.
(i) Type 1-Error
& Type 11-Error
(iii)
SRG-2014
Acceptance Region & Rejection Region.
Q7:(a) Explain what is meant by a statistical hypothesis, Level of significance, Critical Region, Power of a test and
degree of freedom.
SRG-2013
Z-Test(Ϭ is Known for all sample size & Ϭ is Unknown with n≥ 30)
Mean
One Sample & One Population
Q1:-
Given 𝑯𝒐 : 𝝁 ≥ 𝟐𝟎𝟎
and 𝑯𝟏 : 𝝁 < 200, 𝑛 = 100, 𝜶 = 𝟎. 𝟎𝟐𝟑, 𝝈 = 𝟐𝟓. For what value of the sample
mean 𝒙 𝒘𝒊𝒍𝒍 𝒃𝒆 𝒂𝒄𝒄𝒆𝒑𝒕𝒆𝒅.
Q2:-
SRG-2010
A sample of size 40 from a non normal population having mean 72 has sample mean 71 and sample standard
deviation√𝟐𝟎𝟎. Test the hypothesis µ=72 against µ≠ 𝟕𝟐.
SRG-2008/A
Two Sample & Two Population
Q1:Two random samples A & B detailed below were taken from a normal population with standard deviation 0.8.
Test whether difference between means is significant at ∝= 𝟎. 𝟎𝟓.
SRG-2011/A
A
8.5
9.6
10.7
10.9
11.5
11.6
12.8
B
9.3
10.4
10.4
11.9
12.2
12.7
12.9
13.6
T-test(Ϭ is Unknown & n<30)
Two Sample & Two Population
Unpaird Observation
Q1:-
In a test given two groups of students marks obtained were as follows.
SRG-2010
Group-1
15
13
9
14
12
11
8
10
Group-11
12
14
10
9
11
12
10
13
Examine the significance of difference between the two means Take 𝜶 = 𝟎. 𝟎𝟓
Q2:-
Given the following samples from two normally distributed populations with identical standard deviations but
unknown, test H0:- 𝝁𝟏 − 𝝁𝟐 ≤ 𝟑 against H1:- 𝝁𝟏 − 𝝁𝟐 > 3, Let α=0.10.
Sample-1
51, 42, 49, 55, 46, 63, 56, 58, 47, 39, 47
Sample-2
38, 49, 45, 29, 31, 35.
SRG-2012
Q3:- The heights of six randomly selected sailors are in inches:
63, 65, 68, 69, 71 and 72. Those of ten
randomly selected soldiers are 61, 62, 65, 66, 69, 69, 70, 71, 72 and 73. Discuss in the light of these data that the
soldiers are on the average taller than the sailors. Assume that the heights are normally distributed.
SRG-2014
Q4:In a certain experiment to compare two types of sheep food A and B, the following results of increase in
weights were observed.
SRG-2013
Sheep
No.
1
2
3
4
Food A
49
53
51
Food B
52
55
52
5
6
7
8
52
47
50
52
53
53
50
54
54
53
Assuming that the two samples of sheep are independent. Can we conclude the food B is better than Food A?
Paird Observation
Q1:-
The weights of 4 persons before they stopped smoking and 5 weeks after they stopped smoking are as
follows.
SRG-2010
Persons
1
2
3
4
Before
148
178
153
116
After
154
176
151
121
Use the t-test for paired observations to test the hypothesis at 0.05 level of significance, that giving up smoking no
effect on a person’s weight.
Proportion
One Sample & One Population
Q1:-
The manufacturer of a patent medicine claimed that it was 90% effective in relieving an allergy for a period of
8 hours. In a sample of 200 people who had the allergy, the medicine provided relief for 160 people.
Determine whether the manufacturer’s claim is legitimate at =0.01 level.
SRG-2010
Q2:It is claimed that 90% of the men ca not tell the difference between two different brands of cheese, but of the
members of a random sample of 500 men, 72 could distinguish between them. Is the claim justified?
SRG-2012
Q3:-
In 200 tosses of a coin, 115 heads and 85 tails were observed. Test the hypothesis that the coin is fair, using a
level of significance of 0.05.
SRG-2013
B.Sc(Stat) Up to date Papers Chi-Square(2008-2014)
Theory
Q1:-
State the properties of chi-square distribution.
SRG-2010
Q2:Q3:-
what is the difference between association & correlation?
State the important application of 𝝌𝟐 (𝑪𝒉𝒊 𝑺𝒒𝒖𝒂𝒓𝒆) statistic.
SRG-2008/A
SRG-2007/A
Q4:Q5:-
What is coefficient of contingency for an r*c contingency table? Describe its limits. SRG-2008/A
Define standard normal variable. How it is related to 𝝌𝟐 variable.
SRG-2011/A
Q6:Define 𝜒 2 random variable. Explain how you determine a confidence interval estimate of Ϭ2 of a normal
population.
SRG-2014
Q7:-
Discuss the 𝝌𝟐 − 𝒕𝒆𝒔𝒕 𝒐𝒇 𝒈𝒐𝒐𝒅𝒏𝒆𝒔𝒔 𝒐𝒇 𝒇𝒊𝒕. What are the assumptions in the application of these tests to
practical problem?
SRG-2013
Association
Q1:-In 200 tosses of a coin 115 heads were observed. Test the hypothesis that the coin is fair. Use 𝜶 = 𝟎. 𝟎5. SRG-2010
Q2:-
The following figures show the number of births in an area over a year by months of occurrence. SRG-2007/A
January
50579
May
51371
September
52162
February
46472
June
47388
October
50824
March
51419
July
49995
November
47768
April
49670
August
51043
December
51129
Use the 𝝌𝟐 (𝑪𝒉𝒊 𝑺𝒒𝒖𝒂𝒓𝒆) test to discuss whether there is any seasonality in births revealed by these data.
Q3:-
A random sample of 250 men and 250 women were pooled as to their concerning the ownership of television
sets. The following data resulted.
SRG-2012
Classification
Men
Women
Want television
80
120
Do not want television
170
130
Test the hypothesis that the desire to own television set is independent of sex at α =0.05 level of significance.
Binomial Distribution
Q1:-
Following data shows how many times the buses were late arriving at a respective stop in 100 weeks.
No. of times buses were late: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
No of weeks:
0, 2, 8, 19, 29, 26, 13, 3, 0, 0, 0
SRG-2012
Test whether the date follows binomial distribution.
Q2:-
Two hundred digits were chosen at random from a set of tables. The frequencies of the digits were: SRG-2014
Digits
0
1
2
3
4
5
6
7
8
9
Frequency
18
19
23
21
16
25
22
20
21
15
Use the Chi-Square test to assess the correctness of the hypothesis that the digits were distributed in equal number in
the tables from which these were chosen.
Poisson Distribution
Q1:-
Fit a Poisson distribution to the following data and test the goodness of fit at 1% level of significance.
SRG-2010
X=
0
1
2
3
4
5
Y=
12
32
18
8
2
0
Q2:When the first proof of a book containing 250 pages was read, the following distribution of printing mistakes
was found: SRG-2008/A
No. of mistake
0
1
2
3
4
5
per page
frequency
139
76
26
4
2
1
Fit an appropriate distribution to the data and test the goodness of fit.
Q3:Proof reader of a book containing 250 pages constructed the following distribution of mistakes. SRG-2011/A
No. of
Mistakes Per
4
5
0
1
2
3
Page
Frequency
13.9
76
28
4
2
1
Fit an appropriate distribution to the data & test the goodness of fit.
Q4:A medical researcher believes that the standard deviation of the temperature of new born infants is greater
than 0.60. A sample of 15 infants was found to have a standard deviation of 0.80. at ∝= 𝟎. 𝟏𝟎,
does the evidence support the researcher’s belief? Assume that the variable is normally distributed. SRG-2007/A
Variance
Q1:-
A height distribution has a variance Ϭ2 of (2.792)2. Do the following 10 values, selected at random, have a
greater variance than the expected? 67.50, 70.75, 72.00, 63.25, 65.25, 66.75, 69.25, 68.50, 66.50 and 64.75.
SRG-2013
B.Sc(Stat)
Up to date Papers ANOVA(2008-2014)
Theory
Q1:-
(a)
Partition the total sum of squares into error sum of squares and treatment sum of squares. SRG-2010
(b)
Determinations are made on the yield using three methods of catalyzing a chemical process. SRG-2010
Method
Measurements
1
47.3
48.5
49.8
47.9
48.7
11
50.3
49.9
51.6
52.1
51.4
111
49.3
50.2
53.1
50.2
52.1
Do the methods differ significantly at 5% level of significance?
Q2:-
Q3:-
(a)
(b)
what is meant by analysis of variance and degree of freedom?
What are the assumptions underlying a one way analysis of variance?
SRG-2008/A
SRG-2008/A
(c)
Derive the partitioning of degree of freedom for one way analysis of variance.
SRG-2008/A
(a) Derive the partition of the total sum of squares for an analysis of variance in one way classification.
SRG-2011/A
(b)The following data represent marks obtained by five students in the subjects.SRG-2007/A, SRG-2011/A
Subjects
Students
English
Statistics
Economics
1
47
73
61
2
71
88
86
3
71
77
59
4
62
60
66
5
56
95
87
Use at 0.05 level of significance to test the hypothesis that:
(i) The courses are of equal difficulty
(ii)
The students have equal ability
(iii) Apply L.S.D test
Whether the hypothesis is rejected.
Q4:-
(a) Discuss why using multiple two sample t-test is not an appropriate to analysis of variance? Also describe
the assumptions under lying one way analysis of variance.
SRG-2011/A
(b) same as Q26(b)
Q5:-
SRG-2011/A
(a) Derive the partition of total sum of squares for two way analysis of variance without interaction.
(b)Given the following information.
SRG-2012
SRG-2012
Samples
1
2
3
4
No. of Values(ni)
4
6
7
3
Sample means(X-i)
58
57
43
42
Estimate of variances(si2)
10
30.4
5.67
9
Construct an analysis of variance table and test the hypothesis that the population means are equal at α =0.05
Q6:(a) Discuss why using multiple two sample t-test is not an appropriate alternative to Analysis of Variance
(ANOVA). Also give assumptions underlying one way Analysis of Variance.
SRG-2014
(b) Given the data below, test the hypothesis that the means of three populations are equal. SRG-2014
Sample 1
Q7:-
Sample 2
Sample 3
40
70
45
50
65
38
60
66
60
65
50
42
(a) What is meant by analysis of variance? Sketch a table of analysis of variance for two way classification and
define the statistic used to test the significance of difference.
SRG-2013
(b) Three sections of the same elementary mathematics course are taught by three teachers A, B and C. the final
grades were recorded as follows. SRG-2013
A:
91, 84, 45, 82, 75, 68, 47, 95, 38
B:
59, 83, 99, 77, 65, 81, 34, 81, 77, 88, 94, 51, 82
C:
66, 77, 51, 90, 73, 90, 71, 68, 69
Is there a significant difference in the average grades gives by the three teachers? Use the 0.05 level of significance.
B.Sc(Stat)
Up to date Papers Experimental Design(2008-2014)
Theory
Q1:-
Describe in brief the basic principles of experimental design
SRG-2010
Q2:Define a Latin square design. Explain the difference between a Latin square design & randomized complete
block design.
Q3:- Define a Latin Square Design. Explain the difference between a Latin square design and a Randomized
complete block design.
SRG-2007/A
Q4:-
Define the following terms:
(i)
Treatment
(ii)
Experiment Unit.
SRG-2011/A
Q5:We wish to conduct a field experiment to test the yielding ability of 5 verities of wheat. An area of land for 25
plots in available. Give the layout of the following designs.
SRG-2011/A
(i) Completely Randomized Design
(ii)
Randomized Complete Block Design
(iii)Latin Square Design.
Q6 :- Describe a Completely Randomized design, its model and analysis. What are its advantages and
disadvantages?
SRG-2014
Q7:-
Describe the completely randomized design, what are its advantages & disadvantages?
SRG-2012
Q8:-
What is meant by design of experiment? Explain the basic principles of experimentation.
SRG-2013
RCB(One Way ANOVA)
Q1:-
The analysis of variance for RCB design produced the ANOVA table show below.
S.V
d.f
Blocks
5
Treatments
3
Error
S.S
M.S
SRG-2010
F-Ratio
13.80
28.2
34.1
Total
(i) Compute the ANOVA table.
(ii)
Do the data provide sufficient evidence to indicate the difference
among the treatment means taking 𝜶 = 𝟎. 𝟎𝟓
Q2:-
Four treatments given in four blocks in a R.C.B design as below.
Treatment
Blocks
Total
2CS
I
2CN
1CS
And
1CN
1487
II
1134
III
1892
IV
614
Total
819
904
Correction Factor
1840
=1642883
1564
;
5127
Total Sum of Squares=425314
Perform the analysis of variance and compute F. Ratio for treatments.
Q3:-
The following missing observations have been found in ANOVA Table while testing the hypothesis of equality
of “Four Treatment Means”. Determine the missing observations in the table.
SOV
d.f
SS
MS
F.Ratio
Blocks
5
700
-
-
Treatments
-
-
-
8.66
Error
-
-
12.2
-
Total
23
1200
-
-
CRBD(Two Way ANOVA)
Q1:-
Given the following abbreviated analysis of variance for a completely randomized block design: SRG-2007/A
Soure of
Variation
d.f
Sum of Square
Blocks
9
0.4074
Treatments
2
1.1986
Error
27
0.6249
(i) Complete the analysis, fill the mean squares.
(ii)
Mean Squares
Compute the standard error for a treatment mean and
for the difference between two treatment means. (iii)The treatment means are 1.464, 1.195, 1.325 and 1.662.
What mean or means do you suspect might represent different populations.
Q2:The following data give the yields in mounds for four verities each of four blocks in a Randomized Block
experiment. Perform the analysis of variance and test the significance of varietal means. Use α =0.05. SRG-2014
Variety
Blocks
1
2
3
4
1
24.7
16.1
29.1
30.3
2
34.1
16.5
19.1
26.3
3
31
15.4
30.4
19.7
4
24.1
20.7
24.3
23.1
Brand A
2.1
4
6.3
5.4
4.8
3.7
6.1
3.3
Brand B
4.1
0.6
3.1
2.5
4
6.2
1.6
2.2
1.9
5.4
Use the Mann-Whitney test at 5% level of significance to test the hypothesis that the average nicotine content of two
brands are equal against the alternative that they are not equal.
Latin Square Design
Q1:An agricultural experiment was conducted on the Latin Square Plan to test the total effect on yield due to
change of treatments and also to variation of soil in each of two perpendicular directions. The following ANOVA table
was conducted.
SRG-2012
SOV
d.f
SS
MS
F.Ratio
Columns
4
183.7584
-
-
Rows
4
141.0784
-
Treatment
4
-
87.0596
-
Error
12
304.0952
-
-
(i) Complete the ANOVA table and find out if the effect on yield is significant.
(ii) IF the blocking had been done is row & columns, what would have been the conclusions?
Q2:-
Carry out the analysis of variance for the following Latin Square design use α =0.05.
V1
2.3
V2 3.0
V3 3.3
V4 2.5
V2
3.1
V3 4.0
V4 2.4
V1 2.4
V3
2.5
V4 2.5
V1 2.1
V2 2.9
V4
2.6
V1 2.0
V2 2.4
V3 4.4
SRG-2013
B.Sc(Stat) Up to date Papers Correlation & Regression(2008-2014)
Theory
Q1:-
Describes the properties of regression line.
SRG-2010
Q2:-
What is the difference between regression & correlation?
Q3:-
Describe the following concepts (i) Co-efficient of Correlation (ii) Scatter Diagram (iii)Least Square Principle.
SRG-2007/A
Q4:-
Define Co-efficient of determination. What does it measure?
SRG-2011/A
Q5:-
Describe the following (i) Scatter diagram
Least Square Principle
SRG-2012
Q6:-
How will you find a confidence interval for population correlation coefficient?
SRG-2014
(ii)
SRG-2008/A
Regression
Q1:-
Use the following data to test the hypothesis that the regression is linear at 5% level of significance. SRG-2010
X=
2
2
2
3
3
4
4
5
5
6
6
Y=
4
3
8
18
22
24
24
18
13
10
16
Q2:-
Given the following sums:
SRG-2008/A
𝑛 = 10,
∑𝑥𝑖 2 = 193,
(i)
Q3:-
∑𝑥𝑖 = 39,
∑𝑥𝑖𝑦𝑖 = 152.7,
∑𝑦𝑖 = 35.1
∑𝑦𝑖 2 = 130.05
Fit the equation y=a+bx for β=0, use ∝= 𝟎. 𝟎𝟓
(ii)
Find 95% confidence interval for β.
Let bij be the coefficient of linear regression Xi on Xj and we are given:
SRG-2012
N=10, b21=-0.567, b12=-1,741, b23=0.367, b32=0.684, b13=-0.647, b31=-0.392, Calculate r12, r12.3, R1.23 and their significance
Q4:-In a linear regression problem, the following sums were computed from a random sample of size 10. SRG-2014
∑X=320;
∑X2=2400;
∑Y=250;
∑Y2=7230;
∑XY=9415
Use 5% significance level, test the hypothesis that population regression coefficient is greater than 0.5.
Q5:-
Estimate a regression line from the following data of height (X) and weight (Y) of 12 persons.
Height(X)
Weight(Y)
60
110, 135, 120
62
120, 140, 130, 135
64
150, 145
70
170, 185, 160
iii)Test the hypothesis that the population regression coefficients β=0 i.e height and weight are independent, use a
0.05 ii)level of significance.
Correlation
Q1:-From the following information calculate coefficient of correlation and test the significance i.e P=0 at ∝= 𝟎. 𝟎𝟓.
𝑛 = 12, ∑𝑥 = 112, ∑𝑦 =287,
∑𝑥𝑖 2 = 1370, ∑𝑥𝑖𝑦𝑖 = 3073, ∑𝑦𝑖 2 = 12123.
SRG-2008/A
Multiple & Partial Correlation
Q1:Given r12=0.492, r13=0.927, r23=0.758. Find all the partial correlation Co-efficient. Also find the multiple
correlation co-efficient R2.13 of x2 on x1 and x3.
SRG-2007/A
Q2:- Calculate the multiple correlation co-efficient R1.23 and partial correlation coefficient r23.1 from the following
values b12=-0.10
b21=-0.40
b13=0.27
b31=0.60
b23=0.38
b32=0.67.
SRG-2011/A
Q3:-
The simple correlation are given by r12=0.8, r23=-0.9, r13=-0.7. Find all the partial correlation Co-efficient .
B.Sc(Stat) Up to date Papers Non Parameter Statistics(2008-2014)
Theory
Q1:-
How do non parametric test differ from parametric tests?
SRG-2010
Q2:What is meant by vital events? Explain them by giving examples. Define vital statistics; also discuss some of
its uses.
SRG-2008/A
Q3:- Define Non parametric tests, in what sense do they differ from parametric tests? Give some advantages &
disadvantages of Non parametric tests.
SRG-2008/A (b)
Q4:-
Describe the Wilcoxon signed-rank test for one sample. How does it differ from sign test?
Q5:-
Define & explain the following:
(i) Crude death are (ii) Sex Ratio (iii)
SRG-2007/A,SRG-2011/A
Age specific death rate
Q6:-Define the following terms (i) Net Reproduction Rate (ii) Gross Reproduction Rate (iii)Infant Mortality Rate.
SRG-2011/A
Q7:- Define Non parametric tests? Why they are called distribution free tests? Give advantages and disadvantages of
Non Parametric tests.
SRG-2011/A
Q8:- Define & explain the following :(i) Crude death rates(ii) Sex rates (iii)
Age specific death rates. SRG-2012
Q9:- Describe the sign test. When is it most appropriately used? Explain the difference between the Wilcoxon signed
rank test and the sign test.
Numerical
Q1:- Test the null hypothesis that the median of the population from which the data below have been obtained,
equals 55 against the alternative that it is less. Use Wilcoxon sign rank test.
SRG-2010
48
51
49
53
61
59
45
52
65
47
58
57
45
52
53
54
57
46
63
54
49
45
56
65
Q2:-
Compute Specific Morality rates from Cancer per 100, 000 population from the following data. SRG-2010
Age in years Population as of census Death from Cancer
20-29
725369
79
30-39
700213
258
40-49
609616
660
50-59
548400
1585
402054
2342
2872280
3404
60-69
70-over
Q3:-
SRG-2008/A
Age group
Female Population
Death from Cancer
Survival Rate
15-19
8310
1507
0.632
20-24
1510
1835
0.620
25-29
4013
2051
0.0612
30-34
3975
990
0.600
2731
550
40-44
2015
100
45-49
1831
30
35-39
0.530
0.450
Assuming the sex rate at birth 104% calculate.(i) Gross Reproduction Rate (ii) Net Preproduction Rate
Q4:Given the two samples below, test the null hypothesis that the population medians are equal against the
alternative that M1<M2 ∝ at 0.05, by applying Wilcoxon rank sum test.
SRG-2008/A
Samples-1
26,25,38,33,42,40,44,26,25,43,35,48,37
Samples-2
44,30,34,47,35,46,35,47,48,34,32,42,43,49,46,47
Q5:-
Five samples of each of two types of paint are scored as follows
Paint-1
85
87
92
80
84
Paint-11
148
178
153
116
80
Apply this with the Wilcoxon rank-sum test.
Q6:-
Compute the gross and net production rates for the following data:
Female
Population
Female Live birth
15-19
1399
15133
0.9694
20-24
1422
94155
0.9668
25-29
1521
102676
0.9632
30-34
1756
72490
0.9584
35-39
1451
31402
0.9519
40-44
1689
10640
0.9424
45-49
1667
700
0.9279
Age group(Years)
Q7:-
SRG-2007/A,SRG-2011/A
Survival rate
Can a following series of males & females selected from a private firm be considered as a random sample?
FMMFFMFMMMFFFMFMFMMFMFFFMMFMFFMFFMFMFMMF.
SRG-2011/A
Q8:From the following data, calculate gross and net reproduction rates, assuming sex ration at the birth to be
105.2 per cent.
SRG-2012
Female
Registered
Survivor Among
Population
Births
Female out of 100
15-19
8981
1835
634
20-24
5875
2616
602
25-29
3613
2563
568
30-34
3380
1062
530
35-39
3345
558
488
Age
group(years)
40-44
Q9:-
3248
37
444
Ten young recruits were put through a strenuous physical training program by the army. Their weights were
recorded before & after the training with the following results.
Recruit
1
2
3
4
Weight
Before
125
195
160
171
Weight
After
136
201
158
184
Use the Wilcoxon signed rank statistic to test the
5
6
7
8
9
10
140
201
170
170
195
139
145
195
175
190
190
145