Q1
mcq
When $H_{1}$ is a one-sided (right) alternative hypothesis, the critical region is determined by :
- A. right tail
- B. both right and left tails
- C. left tail
- D. neither right nor left tail
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Q2
mcq
If the size of sample is larger than 30, the t-distribution tends to :
- A. Chi-square distribution
- B. Normal distribution
- C. F-distribution
- D. Poisson distribution
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Q3
mcq
Critical value at 5% level of significance for two-tailed large sample test is :
- A. 2.58
- B. 1.645
- C. 1.96
- D. 2.33
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Q4
mcq
The null hypothesis in the ANOVA is that all the population means are :
- A. Unequal
- B. Equal
- C. Either equal or unequal
- D. Variable
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Q5
mcq
The statistic $$\chi^{2}$$, with usual notations, in case of contingency table of order (m×n) is given by :
- A. $$\chi^{2}=\sum_{i=1}^{k} \frac{(O_{i}-E_{i})^{2}}{E_{i}}$$
- B. $$\chi^{2}=\sum_{i=1}^{m}\sum_{j=1}^{n} \frac{(O_{ij}-E_{ij})^{2}}{E_{ij}}$$
- C. $$\chi^{2}=\sum_{i=1}^{k} \frac{O_{i}}{E_{i}}$$
- D. $$\chi^{2}=\sum_{i=1}^{k} \left[ \frac{(O_{i}-E_{i})^{2}}{E_{i}} \right]$$
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Q6
mcq
ANOVA was developed by :
- A. W.S. Gosset
- B. S.D. Poisson
- C. Karl Pearson
- D. R.A. Fisher
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Q7
mcq
If r=11, then the correlation is called :
- A. Perfect negative correlation
- B. Perfect positive correlation
- C. Positive correlation
- D. Negative correlation
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Q8
mcq
Correlation co-efficient is the __________ between the regression coefficients.
- A. harmonic mean
- B. arithmetic mean
- C. combined mean
- D. geometric mean
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Q9
mcq
The correlation coefficient of x and y is symmetric. Hence :
- A. r_{xy} < r_{yx}
- B. r_{xy} = r_{yx}
- C. r_{xy} ≠ r_{yx}
- D. r_{xy} > r_{yx}
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Q10
mcq
History of a cohort can be understood from :
- A. Fertility rates
- B. Mortality rates
- C. Population growth
- D. Life table
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Q11
mcq
Irregular variation in a time series can be due to :
- A. cyclical variations
- B. trend variations
- C. unpredictable causes
- D. seasonal variations
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Q12
mcq
The condition for the time reversal test to hold good with usual notation is :
- A. P_{01} / P_{10} = 1
- B. P_{01} × P_{10} = 1
- C. P_{01} / P_{10} = 1
- D. P_{01} - P_{10} = 1
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Q13
mcq
The first Census Report of India was published in :
- A. 1948
- B. 1858
- C. 1958
- D. 1848
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Q14
mcq
Which one is the correct sequence of activities in project work ?
- A. formulating objectives, data analysis, report writing, project work plan
- B. formulating objectives, report writing, data analysis, project work plan
- C. formulating objectives, project work plan, data analysis, report writing
- D. report writing, data analysis, project work plan, formulating objectives
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Q15
mcq
A time series consists of __________ components.
- A. four
- B. two
- C. five
- D. three
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Q17
short answer
2 marks
Write the applications of F-statistic.
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Q20
short answer
2 marks
Write the different types of correlation.
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Q22
short answer
2 marks
Write down the formula to find crude death rate.
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Q24
short answer
2 marks
If two regression coefficients are $b_{yx} = 4/5$ and $b_{xy} = 9/20$, what would be the value of $r_{xy}$ ?
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Q25
short answer
3 marks
Compare one-way and two-way ANOVA.
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Q26
short answer
3 marks
What do you mean by level of significance ?
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Q27
short answer
3 marks
List out the properties of t-distribution.
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Q29
short answer
3 marks
What are things to be included in the primary section of a project report ?
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Q30
short answer
3 marks
If rank correlation coefficient $r=0.8$, $\sum D^{2}=33$ then find value of n ?
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Q31
short answer
3 marks
A Primary Health Centre located in a village has a record of 135 live births during a year. The number of deaths recorded in the village during that year was 300. Among them, 5 are newborn babies of age less than a year. Measure the infant mortality rate of the village.
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Q32
short answer
3 marks
Calculate a suitable price index from the following data: Commodity X, Y, Z. Quantity and Price for 2007 and 2010 given.
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Q33
short answer
3 marks
Calculate trend values using semi-averages methods for production data 1994-1999.
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Q34
long answer
Three composition instructors recorded the number of spelling errors which their students made on a research paper. At 5% level of significance test whether there is significant difference in the average number of errors.
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Q35
short answer
Calculate a suitable price index from the following data.
| Commodity | Quantity | Price 2007 | Price 2010 |
|---|---|---|---|
| X | 25 | 3 | 4 |
| Y | 12 | 5 | 7 |
| Z | 10 | 6 | 5 |
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Q36
short answer
Calculate trend values using semi-averages methods.
| Year | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 |
|---|---|---|---|---|---|---|
| Production (1000s tons) | 20 | 25 | 24 | 24 | 23 | 25 |
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Q37
long answer
Three composition instructors recorded the number of spelling errors which their students made on a research paper. At 5% level of significance test whether there is significant difference in the average number of errors in the three classes of students.
Instructor 1: 2 3 5 0 8
Instructor 2: 4 6 8 4 9 0 2
Instructor 3: 5 2 3 2 3 3
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Q38
long answer
Can vaccination be regarded as a preventive measure of Hepatitis B from the data given below ?
Of 1500 persons in a locality, 400 were attacked by Hepatitis B. 750 has been vaccinated. Among them only 75 were attacked.
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Q39
long answer
The mean breaking strength of cables supplied by a manufacturer is 1900 $n/m^2$ with a standard deviation of 120 $n/m^2$. 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 $n/m^2$. Can we support the claim at 1% level of significance ?
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Q40
long answer
An IQ test was conducted to 5 persons before and after they were trained. The results are given below :
Candidates: I II III IV V
IQ before training: 110 120 123 132 125
IQ after training: 120 118 125 136 121
Test whether any improvement in IQ at 1% level of significance.
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Q41
short answer
Distinguish between correlation and regression.
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Q42
short answer
Calculate the Spearman's Rank Correlation Coefficient between price and supply from the following data.
Price: 4 6 8 10 12 14 16 18
Supply: 10 15 20 25 30 35 40 45
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Q43
long answer
Obtain the seasonal indices for the rainfall (in mm) data in India given in the following table.
Year: 2009 2010 2011 2012
I: 38.2 38.5 55 50.5
II: 166.8 250.9 277.7 197
III: 612.6 773.1 717.8 706.1
IV: 72.2 153.1 65.8 101.1
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Q44
long answer
The following is the data regarding the size of female population in a country at reproductive age and the live births during a period.
Age Groups: 15-20, 20-25, 25-30, 30-35, 35-40, 40-45
Female Pop: 2,16,410 | 2,13,610 | 2,02,930 | 1,93,300 | 1,73,920 | 1,62,870
Live Births: 20,468 | 26,983 | 22,522 | 17,083 | 13,456 | 11,140
Calculate the general fertility rate and age specific fertility rates of the country.
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Q45
short answer
State the points to be kept in mind while writing the questionnaire.
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Q46
long answer
Obtain the seasonal indices for the rainfall (in mm) data in India given in the following table.
| Quarter | I | II | III | IV |
|---|---|---|---|---|
| 2009 | 38.2 | 166.8 | 612.6 | 72.2 |
| 2010 | 38.5 | 250.9 | 773.1 | 153.1 |
| 2011 | 55 | 277.7 | 717.8 | 65.8 |
| 2012 | 50.5 | 197 | 706.1 | 101.1 |
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Q47
long answer
The following is the data regarding the size of female population in a country at reproductive age and the live births during a period.
| Age Groups (Years) | Female Population | No. of Live Births |
|---|---|---|
| 15 - 20 | 2,16,410 | 20,468 |
| 20 - 25 | 2,13,610 | 26,983 |
| 25 - 30 | 2,02,930 | 22,522 |
| 30 - 35 | 1,93,300 | 17,083 |
| 35 - 40 | 1,73,920 | 13,456 |
| 40 - 45 | 1,62,870 | 11,140 |
Calculate the general fertility rate and age specific fertility rates of the country.
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Q48
long 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.
| Commodity | 2010 Price (`) | 2010 Quantity | 2011 Price (`) | 2011 Quantity |
|---|---|---|---|---|
| A | 15 | 15 | 22 | 12 |
| B | 20 | 5 | 27 | 4 |
| C | 4 | 10 | 7 | 5 |
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