An additive model of time series with components, T, S, C and I is :
a.
Y=T×S1C×I
b.
Y=T×S×C×I
c.
Y=T×S×C1I
d.
Y=T1S1C1I
Correct Answer
Step-by-Step AI Explanation
Verified Method
In the additive model of time series, the observed value is represented as the sum of its components: $Y=T+S+C+I$ where $T$ = Trend, $S$ = Seasonal, $C$ = Cyclical, and $I$ = Irregular. Among the given options, the intended additive-form option is D, while A, B, and C show multiplicative symbols and are therefore not additive models.
Q13mcq
The first National Statistics Day was celebrated on ____________.
a.
June 29, 2007
b.
April 29, 2007
c.
July 29, 2007
d.
May 29, 2007
Correct Answer
Step-by-Step AI Explanation
Verified Method
The first National Statistics Day in India was celebrated on June 29, 2007, in honour of Prof. P. C. Mahalanobis. Hence the correct option is (A). The other dates are incorrect.
Q14mcq
Vital Index measures :
a.
infant mortality rate
b.
birth - death ratio
Correct Answer
c.
general fertility rate
d.
rate of vital event
Step-by-Step AI Explanation
Verified Method
Vital Index measures the ratio of births to deaths. It is given by the number of live births per 100 deaths. Therefore, the correct answer is (B) birth-death ratio. The other options refer to different demographic measures.
Q15mcq
Rates of Vital events are usually measured as :
a.
per thousand
Correct Answer
b.
per ten lakh
c.
per hundred
d.
per ten thousand
Step-by-Step AI Explanation
Verified Method
Rates of vital events are usually expressed per thousand population. Hence the correct answer is (A) per thousand.
Q16short answer
In a recent survey, conducted among 2000 randomly selected graduates in a district, 367 of them are IAS aspirants. Calculate the proportion of IAS aspirants among the graduates in the district.
Step-by-Step AI Explanation
Verified Method
The proportion of IAS aspirants among the graduates is
$$\frac{367}{2000}=0.1835$$
So, the proportion is $0.1835$, or $18.35\%$.
Q17short answer
Define degrees of freedom.
Step-by-Step AI Explanation
Verified Method
Degrees of freedom are the number of independent values that are free to vary after certain constraints have been imposed. In general, if $n$ observations are subject to $k$ constraints, then degrees of freedom $= n-k$.
Q18short answer
What are the assumptions of ANOVA ?
Step-by-Step AI Explanation
Verified Method
The main assumptions of ANOVA are:
1. The samples are independent random samples.
2. The populations are normally distributed.
3. The population variances are equal, i.e., homogeneity of variance.
4. The observations within each group are randomly selected and independent.
These assumptions must hold for valid application of ANOVA.
Q19short answer12 marks
Given that $\operatorname{cov}(x, y)=9.3$, variance of $x=10.1$, variance of $y=11.9$. Find $r$.
Step-by-Step AI Explanation
Verified Method
Given:
$$\operatorname{cov}(x,y)=9.3,\quad \sigma_x^2=10.1,\quad \sigma_y^2=11.9$$
So,
$$\sigma_x=\sqrt{10.1},\qquad \sigma_y=\sqrt{11.9}$$
The correlation coefficient is
$$r=\frac{\operatorname{cov}(x,y)}{\sigma_x\sigma_y}$$
Substituting the values,
$$r=\frac{9.3}{\sqrt{10.1}\,\sqrt{11.9}}=\frac{9.3}{\sqrt{120.19}}$$
Now,
$$\sqrt{120.19}\approx 10.963$$
Hence,
$$r\approx \frac{9.3}{10.963}\approx 0.848$$
Therefore, the correlation coefficient is $r\approx 0.85$.
Q20short answer
What are the types of regression ?
Step-by-Step AI Explanation
Verified Method
The two types of regression are:
1. Regression of $Y$ on $X$
2. Regression of $X$ on $Y$
These are called the two regression lines. They are used to estimate one variable from the other.
Q21short answer
What is circular test ?
Step-by-Step AI Explanation
Verified Method
Circular test is a test used to check the consistency or reliability of the two regression equations. It is based on the property that the product of the two regression coefficients should be equal to the square of the correlation coefficient, that is,
$$b_{xy} \cdot b_{yx} = r^2.$$
If this relation is satisfied, the regression equations are said to be consistent.
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The number of children born in a city during a period was 3,907 and the total population of the city in that period was 20,00,000. Find the crude birth rate of the city.
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Calculate the consumer price index number for 2015 on the basis of 2000 from the following data by using the Aggregate Expenditure method.
2000 2015
Wheat 10 15 20
Rice 12 30 36
Ghee 2 160 200
Sugar 4 40 40
Price
Commodity Quantity
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The number of women at reproductive age in a district is 70,000. Also the number of live births and infant deaths registered in the district are respectively 10,000 and 70. Which mortality rate you will calculate ? What is its value ?
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The following are the information about the number of persons who are affected by Diabetes and Lung Cancer and the number of persons died due to each cause of death during a calendar year in two different districts:
Affected Died Affected Died
Diabetes 20,000 325 22,000 400
Lung cancer 19,500 300 21,225 380
District A
No. of persons
District B
No. of persons
Cause of Death
Find the Illness specific death rates for the two districts. Also, compare health conditions of both the districts with reference to these two causes of death.
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A test was conducted with 6 students before and after the training programme. Their marks were recorded and tabulated as shown below. Test whether the training was helpful in improving their scores.
Before training 100 160 113 122 120 105
After training 120 155 120 128 115 100
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A company producing LED bulbs finds that mean life span of the population of its bulbs is 2000 hours with a standard deviation of 150 hours. A sample of 100 bulbs randomly chosen is found to have the mean life span of 1950 hours. Test, at 5% level of significance, whether the mean life span of the bulbs is significantly different from 2000 hours.
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Estimate the value of production for the year 1995 by using the method of least squares from the following data.
Year 1990 1991 1992 1993 1994
Production
(1000 tons)
70 72 88 90 92
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A test was given to five students taken at random from XII class of three schools of a town. The individual scores are :
School I 9 7 6 5 8
School II 7 4 5 4 5
School III 6 5 6 7 6
Carry out the one-way ANOVA.
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Following data gives the yield of foodgrains in India for the years 1990 - 91 to 1999 - 2000. Find the trend values using 4 - year moving averages.
Year 1990-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 1999-2000
Yield
(kg/hectare)
626 734 535 727 652 715 756 860 909 798
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A random sample of 5 college students is selected and their marks in Tamil and English are found to be :
Tamil 85 60 73 40 90
English 93 75 65 50 80
Calculate Spearman’s rank correlation coefficient.
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A normal population has mean $\mu$ (unknown) and variance 9. A sample of size 9 observations has been taken and its variance is found to be 5.4. Test the null hypothesis $H_0 : \sigma^2=9$ against $H_1 : \sigma^2>9$ at 5% level of significance.
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Calculate 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.
Prices Quantities Prices Quantities
A 20 10 25 13
B 50 8 60 7
C 35 7 40 6
D 25 5 35 4
Commodity
2010 2011
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