LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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FIFTH SEMESTER – November 2008
ST 5503 – COMPUTATIONAL STATISTICS
Date : 10-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
Answer ALL the Questions. Each question carries 20 marks.
- The table given below presents the data for complete census of 2010 farms in a region. The farms were stratified according to farm-size in acres into seven strata. The number of farms in the different strata, the strata standard deviation are given below. Find the sample sizes under each stratum under (i) Proportional allocation and (ii) Neyman Optimum allocation.
| Stratum No. | No. of farms | Stratum standard deviation |
| 1 | 394 | 8.3 |
| 2 | 461 | 13.3 |
| 3 | 391 | 15.1 |
| 4 | 334 | 19.8 |
| 5 | 169 | 24.5 |
| 6 | 113 | 26 |
| 7 | 148 | 35.2 |
(OR)
In a population size N = 6, the values of Yi are 24, 56, 12, 45, 25, 55. Calculate the sample mean for all possible simple random samples (without replacement) of size n = 2, also calculate s 2 for all samples and verify E (s 2 ) = S 2.
- Calculate fixed base index numbers and chain base index numbers for the
following data.
| Commodity | 2002 | 2003 | 2004 | 2005 | 2006 |
| I | 2 | 3 | 5 | 7 | 8 |
| II | 8 | 10 | 12 | 4 | 18 |
| III | 4 | 5 | 7 | 9 | 12 |
(OR)
Calculate seasonal variations given the average quarterly price of a commodity for
5 years by ratio to trend method.
| Year | I Quarter | II Quarter | III Quarter | IV Quarter |
| 2001 | 28 | 22 | 22 | 28 |
| 2002 | 35 | 28 | 25 | 36 |
| 2003 | 33 | 34 | 30 | 35 |
| 2004 | 31 | 31 | 27 | 35 |
| 2005 | 37 | 36 | 31 | 36 |
- (a) Glaucoma is an eye disease that is manifested by high intraocular pressure. The
distribution of intraocular pressure in the general population is known to be normal
with mean 16 mm Hg and standard deviation 3 mm Hg. Pressures in the range of 12
mm Hg to 20 mm Hg are considered safe. What percentage of the population is
unsafe?
&
(b) The scores in a certain test from 12 men and 10 women candidates are reported below:
Men: 56, 67, 45, 78, 86, 64, 78, 88, 91, 46, 45, 84
Women: 67, 48, 91, 75, 58, 90, 46, 69, 70, 82
Test whether there is significant difference in the average scores of the two groups at 5% level of significance. (Variances are considered to be equal but are not known)
(6 + 14)
(OR)
(c) In a pediatric clinic a study is carried out to test the effectiveness of aspirin in
reducing temperatures. The temperatures of twelve five-year old children suffering
from influenza were observed before and after one hour of administering aspirin and
the paired observations are reported below:
| Patient | Temp ( 0F) before
taking aspirin |
Temp (0F) 1 hr
after taking aspirin |
| 1
2 3 4 5 6 7 8 9 10 11 12 |
102.4
103.2 101.9 103.0 101.2 100.7 102.5 103.1 102.8 102.3 101.9 101.4 |
99.6
100.1 100.2 101.1 99.8 100.2 101.0 100.1 100.7 101.1 101.3 100.2 |
Test whether aspirin is effective in reducing the temperature at 5% level of
significance.
&
(d) A textile mill attempts to control the yarn defects that appear on manufactured
cloth. The occurrence of defects has been found to follow Poisson law and the
historical average number of defects per 100 m of cloth is 1.25. Recently, due to
changes implemented by the HR department, the occurrence of defects is expected
to reduce significantly. The quality control department wishes to test whether this
improvement has happened. The following numbers of defects were observed from
12 bales of cloth (each of length 100 m): 1, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1. Carry out the
relevant test at 5% level of significance and report your findings to the quality
control department. (8 +12)
- (a) The daily iron intake among children in the age group 9 – 11 has been
established to be normally distributed with average14.4 mg and standard deviation
4.75 mg. A social service organization working among ‘Below-Poverty-Line’
(BPL) families, took a sample of 50 children and reported that the average intake
among them was 12.5 mg. It is believed that the standard deviation is not different
(from the known 4.75 mg) for this group. Does this information indicate that the
iron intake is significantly lower in the BPL families?
&
(b) In a study on infarct size among people, the following data were obtained from 6
treated children and 8 untreated children:
Treated Children: 20.3, 21.0, 21.4, 18.9, 19.5, 19.7
Untreated Children: 19.6, 18.7, 19.9, 20.6, 20.1, 19.6, 19.0, 21.0
Test whether the variances differ significantly at 2% level of significance
(6 + 14)
(OR)
(c) A small factory A produces fasteners for use in machine tools and supplies it to a machine tool manufacturing company B. Factory A supplies fasteners in large lots every day and maintains a low percentage of 5% defectives. Company B carries out sampling inspection every day by taking a sample of 20 fasteners. It rejects the entire lot and sends it back to Factory A if more than one defective is observed in the sample. Find the proportion of days in which lots are sent back to factory A.
&
(d) The dispersion in the quality characteristic is an important indicator of the quality conformance of a production process. It has been historically found that a production process was operating with a variance of 18 for a normally distributed quality characteristic, But, due to certain changes made in the processes, it is believed that there could be a change in the process dispersion. The following data on the quality characteristic are available after the changes were implemented:
65, 60, 67, 70, 67, 62, 68, 63, 59, 69, 70, 58, 75, 75, 78
Test whether there is a significant change in the process variance at 1% level of
significance. ( 8 +12)
- The following are the weight gains (pounds) of two random samples of young Indians fed on two different diets but otherwise kept under identical conditions:
Diet I: 16.3 10.1 10.7 13.5 14.9 11.8 14.3 10.2 12.0 14.7 23.6 15.1 14.5 18.4 13.2 14.0
Diet II: 21.3 23.8 15.4 19.6 12.0 13.9 18.8 19.2 15.3 20.1 14.8 18.9 20.7 21.1 15.8 16.2
Use U test at 0.01 level of significance to test the null hypothesis that the two population samples are identical against the alternative hypothesis that on the average the second diet produces a greater gain in weight.
(OR)
The same mathematics papers were marked by three teachers A, B and C. The final marks were recorded as follows:
| Teacher A | 73 | 89 | 82 | 43 | 80 | 73 | 66 | 60 | 45 | 93 | 36 | 77 |
| Teacher B | 88 | 78 | 48 | 91 | 51 | 85 | 74 | 77 | 31 | 78 | 62 | 76 |
| Teacher C | 68 | 79 | 56 | 91 | 71 | 71 | 87 | 41 | 59 | 68 | 53 | 79 |
Use Kruskal-wallis test, at the 0.05 level of significance to determine if the marks distributions given by the three teachers differ significantly. (10 + 10)
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