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Q1
mcq
1 mark
When the alternative hypothesis is $H_1 : \mu \ne \mu_0$, the critical region will be determined by :
-
A.
right tail
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B.
both right and left tails
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C.
left tail
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D.
neither right nor left tail
Correct Answer: B —
Solution
When $H_1: \mu \ne \mu_0$, it is a two-tailed test, so the critical region lies in both the right and left tails of the sampling distribution. Hence, option (b) is correct. Options (a) and (c) are for one-tailed tests, and (d) is incorrect because there must be a rejection region in a two-sided test.
Q2
mcq
1 mark
What is level of significance ?
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A.
Upper limit of $P$ (Type I Error)
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B.
$P$ (Type I Error)
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C.
Upper limit of $P$ (Type II Error)
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D.
$P$ (Type II Error)
Correct Answer: A —
Solution
The level of significance is the upper limit of the probability of committing Type I error, that is, rejecting a true null hypothesis. It is usually denoted by $\alpha$. Therefore, option (a) is correct. Options (b), (c), and (d) are incorrect because Type II error is denoted by $\beta$, not the level of significance.
Q3
mcq
1 mark
If $n$ is the degree of freedom of chi-square distribution then its variance is :
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A.
$2n$
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B.
$n$
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C.
$n11$
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D.
$n-1$
Correct Answer: A —
Solution
For a chi-square distribution with $n$ degrees of freedom, the variance is $2n$. So the correct answer is (a). The mean is $n$, not the variance, and the other options are incorrect.
Q4
mcq
1 mark
In two-way classification the total variation TSS =
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A.
$SST1SSB-SSE$
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B.
$SST1SSB1SSE$
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C.
$SST1SSB$
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D.
$SST-SSB1SSE$
Correct Answer: C —
Solution
In two-way classification, the total sum of squares is partitioned into row variation and column variation. Hence, $TSS = SST + SSB$. Therefore, option (c) is correct. The other options include the error sum of squares incorrectly or do not represent the correct partition.
Q5
mcq
1 mark
F-statistic is the ratio of two Independent sample __________.
-
A.
Standard deviation
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B.
Mean
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C.
Mode
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D.
Variances
Correct Answer: D —
Solution
The F-statistic is defined as the ratio of two independent sample variances. Therefore, option (d) is correct. It is not the ratio of means, standard deviations, or modes.
Q6
mcq
1 mark
If $\Sigma D^2 = 0$, rank correlation is :
Q7
mcq
1 mark
If $r=0$ then $\operatorname{cov}(x,y)$ is :
Q8
mcq
1 mark
__________ is the Father of mental tests.
-
A.
Francis Galton
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B.
R.A. Fisher
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C.
A.L. Bowley
-
D.
Croxton and Cowden
Q9
mcq
1 mark
The regression lines intersect at :
-
A.
$(0,0)$
-
B.
$(X,Y)$
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C.
$(1,1)$
-
D.
$(X,Y)$
Q10
mcq
1 mark
The condition for the circular test to hold good with usual notation is :
-
A.
$P_{01}÷P_{10}=1$
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B.
$P_{01}×P_{10}=1$
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C.
$P_{01}1P_{12}1P_{20}=1$
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D.
$P_{01}×P_{12}×P_{20}=1$
Q11
mcq
1 mark
The consumer price index in 2000 increases by 80% as compared to the base 1990. A person getting Rs. 60,000 per annum in 1990 should now (in 2000) get :
-
A.
Rs. 1,18,000 p.a.
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B.
Rs. 1,08,000 p.a.
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C.
Rs. 1,80,000 p.a.
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D.
Rs. 1,02,000 p.a.
Q12
mcq
1 mark
Cyclical movements are due to :
-
A.
trend
-
B.
ratio to trend
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C.
trade cycle
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D.
seasonal
Q13
mcq
1 mark
The first Economic census was conducted in __________.
-
A.
1977
-
B.
1957
-
C.
1987
-
D.
1967
Q14
mcq
1 mark
NSSO publishes the bi-annual journal :
-
A.
Pramana
-
B.
Sarvekshana
-
C.
Yojana
-
D.
Sankhya
Q15
mcq
1 mark
Qualitative data implies :
-
A.
non-measurable
-
B.
partly measurable
-
C.
measurable
-
D.
all the above
Q16
short answer
The mean breaking strength of cables supplied by a manufacturer is 1900 n/m² with a Standard Deviation of 120 n/m². The manufacturer introduced a new technique in the manufacturing process and claimed that the breaking strength of the cables has increased. In order to test the claim, a sample of 60 cables is tested. It is found that the mean breaking strength of the sampled cables is 1960 n/m². Can we support the claim at 1% level of significance?
Q17
short answer
The number of pages typed by 5 DTP-Operators for 1 hour in the morning sessions are 10, 12, 13, 8, 9 and the number of pages typed by them for 1 hour in the afternoon are 11, 15, 12, 10, 8. Is there any significant difference in the mean number of pages typed?
Q18
short answer
Three different techniques namely medication, exercises and special diet are randomly assigned to individuals diagnosed with high blood pressure to lower the blood pressure. After four weeks the reduction in each person's blood pressure is recorded. Test at 5% level, whether there is significant difference in mean reduction of blood pressure among the three techniques.
Medication 10 12 9 15 13
Exercise 6 8 3 0 2
Special Diet 5 9 12 8 4
Q19
short answer
The following table gives quarterly expenditure over a number of years. Obtain seasonal indices for the data.
Year
Season
I 78 84 92 100
II 62 64 70 81
III 56 61 63 72
IV 71 82 83 96
2000 2001 2002 2003
Q20
short answer
Find the linear regression equation of percentage of worms (Y) on size of the crop (X) based on the following seven observations.
Size of the crop (X) 16 15 11 27 39 22 20
Percentage of worms (Y) 24 25 34 40 35 20 23
Q21
short answer
Number of deaths recorded in various age groups in two areas and the population size in each age group are given in the following table. Population No. of Deaths Population No. of Deaths 0-10 3000 55 7500 300 10-25 4500 30 6000 50 25-45 6000 40 8000 40 45 and over 1000 15 2000 64 Area-I Area-II Age Group (in years) Find the crude death rates and age specific death rates of Area I and Area II.
Q22
short answer
A survey was conducted with 500 female students of which 60% were intelligent, 40% had uneducated fathers, while 30% of the not intelligent female students had educated fathers. Test the hypothesis that the education of fathers and intelligence of female students are independent.
Q23
short answer
Construct the price indices from the following data by applying (1) Laspeyre's method (2) Paasche's method and (3) Fisher ideal number by taking 2010 as the base year.
Price (`) Quantity Price (`) Quantity
A 15 15 22 12
B 20 5 27 4
C 4 10 7 5
2010 2011
Commodity
Q24
short answer
Construct the price indices from the following data by applying (1) Laspeyre's method (2) Paasche's method and (3) Fisher ideal number by taking 2010 as the base year.
Q26
short answer
Following data gives the yield of wheat in India for the years 2010-11 to 2019-20. Find the trend values using 3-year moving averages.
Year 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20
Yield (kg/hectare)
626 734 535 727 652 715 756 860 909 798
Q38
short answer
Calculate the Spearman's rank correlation coefficient for the following data.
Marks in Statistics 82 70 95 60 55
Marks in Economics 65 72 45 33 84
