Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 8th Sem New 2180403 Biostatistics Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
2
Q.3 (a) What is inferential biostatistics and how is it different from descriptive biostat? 03
(b) Calculate the mean from the following data:
Fish
Length
90-99 80-89 70-79 60-69 50-59 40-49 30-39
In cms
Frequency
2 12 22 20 14 4 1
04
(c) Two samples A and B have means 2.158 and 1.96 respectively. Determine whether
there is significant difference in means of sample A and sample B.
Sample
A
2.5 2.1 1.9 2.4 1.8 2.6 2.5 2.3 0.9 1.7 2.2 2.0
Sample
B
1.8 1.7 1.9 2.2 2.3 2.0 1.9 1.8 2.1 1.9 - -
07
OR
Q.3 (a) Write a note on: Importance of Biostatistics 03
(b) The following table gives the age distribution of a group of 50 individuals. Calculate
the coefficient of range in this group.
Age (in years) X 16-20 21-25 26-30 31-35
No of persons f
10 15 17 8
04
(c) Body length of 10 fishes of a species of fish population was recorded from two
ponds in the following table:
Pond Body length of fishes in cm
A 20 24 20 28 22 20 24 32 34 26
B 12 10 8 10 6 4 14 20 10 6
Calculate the mean difference in total body length between the fishes in the above
two ponds is significant or not.
07
Q.4 (a) Write a note on methods of least square. 03
(b) Explain the type-I and type- II errors. 04
(c) In a clinical treatment, the patients were tested to see the effect of a potential
hypertensive drug. The 50 patients were assigned to receive drug and other 50 as
placebo at random. Their response to treatment was categorized as favorable or
unfavorable. The data is given in the table below:
Treatment Response Total
Un favorable Favorable
Placebo 41 9 50
Drug 16 34 50
57 34 100
07
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
2
Q.3 (a) What is inferential biostatistics and how is it different from descriptive biostat? 03
(b) Calculate the mean from the following data:
Fish
Length
90-99 80-89 70-79 60-69 50-59 40-49 30-39
In cms
Frequency
2 12 22 20 14 4 1
04
(c) Two samples A and B have means 2.158 and 1.96 respectively. Determine whether
there is significant difference in means of sample A and sample B.
Sample
A
2.5 2.1 1.9 2.4 1.8 2.6 2.5 2.3 0.9 1.7 2.2 2.0
Sample
B
1.8 1.7 1.9 2.2 2.3 2.0 1.9 1.8 2.1 1.9 - -
07
OR
Q.3 (a) Write a note on: Importance of Biostatistics 03
(b) The following table gives the age distribution of a group of 50 individuals. Calculate
the coefficient of range in this group.
Age (in years) X 16-20 21-25 26-30 31-35
No of persons f
10 15 17 8
04
(c) Body length of 10 fishes of a species of fish population was recorded from two
ponds in the following table:
Pond Body length of fishes in cm
A 20 24 20 28 22 20 24 32 34 26
B 12 10 8 10 6 4 14 20 10 6
Calculate the mean difference in total body length between the fishes in the above
two ponds is significant or not.
07
Q.4 (a) Write a note on methods of least square. 03
(b) Explain the type-I and type- II errors. 04
(c) In a clinical treatment, the patients were tested to see the effect of a potential
hypertensive drug. The 50 patients were assigned to receive drug and other 50 as
placebo at random. Their response to treatment was categorized as favorable or
unfavorable. The data is given in the table below:
Treatment Response Total
Un favorable Favorable
Placebo 41 9 50
Drug 16 34 50
57 34 100
07
3
OR
Q.4 (a) What is probable error? 03
(b) Find the coefficient of rank correlation from the data given below showing the ranks
of 10 students according to their performance in Microbiology and Statistics.
Rank in
Microbiology
8 3 9 2 7 10 4 6 1 5
Rank in
Statistics
9 5 10 1 8 7 3 4 2 6
04
(c) In a sample survey of public opinion, two questions were asked: they were : (1) do
you drink? (2) are you in favour of local opinion of sale of liquor? The answers of
the survey is given in the local table. Is local opinion on the sale of liquor is
dependent on the individual habit of drinking?
Yes No
Row
Total
Yes 56 31 87
No 18 6 24
Column Total 74 37 111
07
Q.5 A company appoints 4 salesmen observe the sales in 3 seasons. Carry put ANOVA
to check the difference in sales due to salesman and seasons. The details are given
below.
SALESMEN
Seasons
A B C D
Summer 36 36 21 35
Winter 28 29 31 32
Monsoon 26 28 29 24
14
OR
Q.5
The following data represent the numbers of unit of production per day turned out by 4
different workers using 5 different types of machines:
Worker A B C D E
1 4 5 3 6 7
2 6 8 6 5 4
3 7 6 7 8 8
4 3 5 4 8 2
On the basis of this information, can it be concluded that
(i) The productivity is the same for different machines?
(ii) The workers do not differ with regard to productivity?
14
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
2
Q.3 (a) What is inferential biostatistics and how is it different from descriptive biostat? 03
(b) Calculate the mean from the following data:
Fish
Length
90-99 80-89 70-79 60-69 50-59 40-49 30-39
In cms
Frequency
2 12 22 20 14 4 1
04
(c) Two samples A and B have means 2.158 and 1.96 respectively. Determine whether
there is significant difference in means of sample A and sample B.
Sample
A
2.5 2.1 1.9 2.4 1.8 2.6 2.5 2.3 0.9 1.7 2.2 2.0
Sample
B
1.8 1.7 1.9 2.2 2.3 2.0 1.9 1.8 2.1 1.9 - -
07
OR
Q.3 (a) Write a note on: Importance of Biostatistics 03
(b) The following table gives the age distribution of a group of 50 individuals. Calculate
the coefficient of range in this group.
Age (in years) X 16-20 21-25 26-30 31-35
No of persons f
10 15 17 8
04
(c) Body length of 10 fishes of a species of fish population was recorded from two
ponds in the following table:
Pond Body length of fishes in cm
A 20 24 20 28 22 20 24 32 34 26
B 12 10 8 10 6 4 14 20 10 6
Calculate the mean difference in total body length between the fishes in the above
two ponds is significant or not.
07
Q.4 (a) Write a note on methods of least square. 03
(b) Explain the type-I and type- II errors. 04
(c) In a clinical treatment, the patients were tested to see the effect of a potential
hypertensive drug. The 50 patients were assigned to receive drug and other 50 as
placebo at random. Their response to treatment was categorized as favorable or
unfavorable. The data is given in the table below:
Treatment Response Total
Un favorable Favorable
Placebo 41 9 50
Drug 16 34 50
57 34 100
07
3
OR
Q.4 (a) What is probable error? 03
(b) Find the coefficient of rank correlation from the data given below showing the ranks
of 10 students according to their performance in Microbiology and Statistics.
Rank in
Microbiology
8 3 9 2 7 10 4 6 1 5
Rank in
Statistics
9 5 10 1 8 7 3 4 2 6
04
(c) In a sample survey of public opinion, two questions were asked: they were : (1) do
you drink? (2) are you in favour of local opinion of sale of liquor? The answers of
the survey is given in the local table. Is local opinion on the sale of liquor is
dependent on the individual habit of drinking?
Yes No
Row
Total
Yes 56 31 87
No 18 6 24
Column Total 74 37 111
07
Q.5 A company appoints 4 salesmen observe the sales in 3 seasons. Carry put ANOVA
to check the difference in sales due to salesman and seasons. The details are given
below.
SALESMEN
Seasons
A B C D
Summer 36 36 21 35
Winter 28 29 31 32
Monsoon 26 28 29 24
14
OR
Q.5
The following data represent the numbers of unit of production per day turned out by 4
different workers using 5 different types of machines:
Worker A B C D E
1 4 5 3 6 7
2 6 8 6 5 4
3 7 6 7 8 8
4 3 5 4 8 2
On the basis of this information, can it be concluded that
(i) The productivity is the same for different machines?
(ii) The workers do not differ with regard to productivity?
14
4
Selected values of normal distributions
Level of significance Z value- two tailed test Z value- one tailed test
0.10 1.645 1.282
0.05 1.96 1.645
0.02 2.326 2.054
0.01 2.576 2.326
0.001 3.291 3.090
Table : Values of F at the 5% Significance Level
DoF- denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 161 200 216 225 230 234 237 239 241
2 18.50 19.00 19.20 19.20 19.30 19.30 19.40 19.40 19.40
3 10.10 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
4 7.71 6.40 6.59 6.39 6.26 6.16 6.09 6.04 6.00
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80.
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
30 4.17 .3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
Table: Values of F at The 1% Significance Level
DoF-denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 4052 5000 5403 5625 5764 5859 5928 5982 6022
2 98.50 99.90 99.20 99.20 99.30 99.30 99.40 99.40 99.40
3 34.10 30.80 29.50 28.70 28.20 27.09 27.70 27.50 27.30
4 21.20 18.00 16.70 16.00 15.50 15.20 15.00 14.80 14.70
6 13.70 10.90 9.78 9.15 8.75 8.47 8.26 8.10 7.98
8 11.30 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91
10 10.00 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39
14 8.86 6.51 5.56 5.04 4.70 4.46 4.28 4.14 4.03
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
2
Q.3 (a) What is inferential biostatistics and how is it different from descriptive biostat? 03
(b) Calculate the mean from the following data:
Fish
Length
90-99 80-89 70-79 60-69 50-59 40-49 30-39
In cms
Frequency
2 12 22 20 14 4 1
04
(c) Two samples A and B have means 2.158 and 1.96 respectively. Determine whether
there is significant difference in means of sample A and sample B.
Sample
A
2.5 2.1 1.9 2.4 1.8 2.6 2.5 2.3 0.9 1.7 2.2 2.0
Sample
B
1.8 1.7 1.9 2.2 2.3 2.0 1.9 1.8 2.1 1.9 - -
07
OR
Q.3 (a) Write a note on: Importance of Biostatistics 03
(b) The following table gives the age distribution of a group of 50 individuals. Calculate
the coefficient of range in this group.
Age (in years) X 16-20 21-25 26-30 31-35
No of persons f
10 15 17 8
04
(c) Body length of 10 fishes of a species of fish population was recorded from two
ponds in the following table:
Pond Body length of fishes in cm
A 20 24 20 28 22 20 24 32 34 26
B 12 10 8 10 6 4 14 20 10 6
Calculate the mean difference in total body length between the fishes in the above
two ponds is significant or not.
07
Q.4 (a) Write a note on methods of least square. 03
(b) Explain the type-I and type- II errors. 04
(c) In a clinical treatment, the patients were tested to see the effect of a potential
hypertensive drug. The 50 patients were assigned to receive drug and other 50 as
placebo at random. Their response to treatment was categorized as favorable or
unfavorable. The data is given in the table below:
Treatment Response Total
Un favorable Favorable
Placebo 41 9 50
Drug 16 34 50
57 34 100
07
3
OR
Q.4 (a) What is probable error? 03
(b) Find the coefficient of rank correlation from the data given below showing the ranks
of 10 students according to their performance in Microbiology and Statistics.
Rank in
Microbiology
8 3 9 2 7 10 4 6 1 5
Rank in
Statistics
9 5 10 1 8 7 3 4 2 6
04
(c) In a sample survey of public opinion, two questions were asked: they were : (1) do
you drink? (2) are you in favour of local opinion of sale of liquor? The answers of
the survey is given in the local table. Is local opinion on the sale of liquor is
dependent on the individual habit of drinking?
Yes No
Row
Total
Yes 56 31 87
No 18 6 24
Column Total 74 37 111
07
Q.5 A company appoints 4 salesmen observe the sales in 3 seasons. Carry put ANOVA
to check the difference in sales due to salesman and seasons. The details are given
below.
SALESMEN
Seasons
A B C D
Summer 36 36 21 35
Winter 28 29 31 32
Monsoon 26 28 29 24
14
OR
Q.5
The following data represent the numbers of unit of production per day turned out by 4
different workers using 5 different types of machines:
Worker A B C D E
1 4 5 3 6 7
2 6 8 6 5 4
3 7 6 7 8 8
4 3 5 4 8 2
On the basis of this information, can it be concluded that
(i) The productivity is the same for different machines?
(ii) The workers do not differ with regard to productivity?
14
4
Selected values of normal distributions
Level of significance Z value- two tailed test Z value- one tailed test
0.10 1.645 1.282
0.05 1.96 1.645
0.02 2.326 2.054
0.01 2.576 2.326
0.001 3.291 3.090
Table : Values of F at the 5% Significance Level
DoF- denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 161 200 216 225 230 234 237 239 241
2 18.50 19.00 19.20 19.20 19.30 19.30 19.40 19.40 19.40
3 10.10 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
4 7.71 6.40 6.59 6.39 6.26 6.16 6.09 6.04 6.00
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80.
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
30 4.17 .3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
Table: Values of F at The 1% Significance Level
DoF-denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 4052 5000 5403 5625 5764 5859 5928 5982 6022
2 98.50 99.90 99.20 99.20 99.30 99.30 99.40 99.40 99.40
3 34.10 30.80 29.50 28.70 28.20 27.09 27.70 27.50 27.30
4 21.20 18.00 16.70 16.00 15.50 15.20 15.00 14.80 14.70
6 13.70 10.90 9.78 9.15 8.75 8.47 8.26 8.10 7.98
8 11.30 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91
10 10.00 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39
14 8.86 6.51 5.56 5.04 4.70 4.46 4.28 4.14 4.03
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72
5
Table value of ?t? at different degrees of freedom on P=0.05 and 0.01 level
V
P
0.05 0.01
1 6.314 31.821
2 2.920 6.965
3 2.353 4.541
4 2.132 3.747
5 2.015 3.365
6 1.943 3.143
7 1.895 2.998
8 1.860 2.896
9 1.833 2.821
10 1.812 2.764
11 1.796 2.718
12 1.782 2.681
13 1.771 2.650
14 1.761 2.624
15 1.753 2.602
16 1.746 2.583
17 1.740 2.567
18 1.734 2.552
19 1.729 2.541
20 1.725 2.528
21 1.721 2.518
22 1.717 2.508
23 1.714 2.500
24 1.711 2.492
25 1.708 .2.485
26 1.706 2.479
27 1.703 2.463
28 1.701 2.467
29 1.699 2.462
30 1.697 2.457
40 1.684 2.423
60 1.671 2.390
120 1.658 2.338
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2180403 Date: 29/11/2018
Subject Name: Biostatistics
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks
4. All the necessary charts are pasted with this question paper.
5. Notations used in this paper, carry conventional meaning.
MARKS
Q.1 (a) Differentiate between histogram, pie chart, bat chart and map diagram. 03
(b) Distinguish between Mean, Median and Mode. 04
(c) The viable cell count for the Acetobacter (N) in a culture after t hours, is given by the
following table :
t 0 1 2 3 4 5 6
N 30 45 65 90 130 190 270
Fit a curve of the form N= ab
t
and estimate N when t = 5.5 .
07
Q.2 (a) Define : 1. Quartiles 2. Deciles 3. Quintiles. 03
(b) The frequency distribution of weight in grams of mangoes of a given variety is
given below. Calculate the arithmetic mean and the median.
Weight in grams Number of mangoes
410-419 14
420-429 20
430-439 42
440-449 54
450-459 45
460-469 18
470-479 7
04
(c) At an international student organization the president of organization expected that
the students present should be 10 percent Africans, 25 percent Indians, 40 percent
Asians and 25 percent Americans. The students actually present consisted of 25
Africans, 15 Indians, 80 Asians and 20 Americans. Test the president?s belief at 5
percent level.
07
OR
(c) Find the coefficient of correlation between the variables X and Y using Karl
Pearson?s method:
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
07
2
Q.3 (a) What is inferential biostatistics and how is it different from descriptive biostat? 03
(b) Calculate the mean from the following data:
Fish
Length
90-99 80-89 70-79 60-69 50-59 40-49 30-39
In cms
Frequency
2 12 22 20 14 4 1
04
(c) Two samples A and B have means 2.158 and 1.96 respectively. Determine whether
there is significant difference in means of sample A and sample B.
Sample
A
2.5 2.1 1.9 2.4 1.8 2.6 2.5 2.3 0.9 1.7 2.2 2.0
Sample
B
1.8 1.7 1.9 2.2 2.3 2.0 1.9 1.8 2.1 1.9 - -
07
OR
Q.3 (a) Write a note on: Importance of Biostatistics 03
(b) The following table gives the age distribution of a group of 50 individuals. Calculate
the coefficient of range in this group.
Age (in years) X 16-20 21-25 26-30 31-35
No of persons f
10 15 17 8
04
(c) Body length of 10 fishes of a species of fish population was recorded from two
ponds in the following table:
Pond Body length of fishes in cm
A 20 24 20 28 22 20 24 32 34 26
B 12 10 8 10 6 4 14 20 10 6
Calculate the mean difference in total body length between the fishes in the above
two ponds is significant or not.
07
Q.4 (a) Write a note on methods of least square. 03
(b) Explain the type-I and type- II errors. 04
(c) In a clinical treatment, the patients were tested to see the effect of a potential
hypertensive drug. The 50 patients were assigned to receive drug and other 50 as
placebo at random. Their response to treatment was categorized as favorable or
unfavorable. The data is given in the table below:
Treatment Response Total
Un favorable Favorable
Placebo 41 9 50
Drug 16 34 50
57 34 100
07
3
OR
Q.4 (a) What is probable error? 03
(b) Find the coefficient of rank correlation from the data given below showing the ranks
of 10 students according to their performance in Microbiology and Statistics.
Rank in
Microbiology
8 3 9 2 7 10 4 6 1 5
Rank in
Statistics
9 5 10 1 8 7 3 4 2 6
04
(c) In a sample survey of public opinion, two questions were asked: they were : (1) do
you drink? (2) are you in favour of local opinion of sale of liquor? The answers of
the survey is given in the local table. Is local opinion on the sale of liquor is
dependent on the individual habit of drinking?
Yes No
Row
Total
Yes 56 31 87
No 18 6 24
Column Total 74 37 111
07
Q.5 A company appoints 4 salesmen observe the sales in 3 seasons. Carry put ANOVA
to check the difference in sales due to salesman and seasons. The details are given
below.
SALESMEN
Seasons
A B C D
Summer 36 36 21 35
Winter 28 29 31 32
Monsoon 26 28 29 24
14
OR
Q.5
The following data represent the numbers of unit of production per day turned out by 4
different workers using 5 different types of machines:
Worker A B C D E
1 4 5 3 6 7
2 6 8 6 5 4
3 7 6 7 8 8
4 3 5 4 8 2
On the basis of this information, can it be concluded that
(i) The productivity is the same for different machines?
(ii) The workers do not differ with regard to productivity?
14
4
Selected values of normal distributions
Level of significance Z value- two tailed test Z value- one tailed test
0.10 1.645 1.282
0.05 1.96 1.645
0.02 2.326 2.054
0.01 2.576 2.326
0.001 3.291 3.090
Table : Values of F at the 5% Significance Level
DoF- denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 161 200 216 225 230 234 237 239 241
2 18.50 19.00 19.20 19.20 19.30 19.30 19.40 19.40 19.40
3 10.10 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
4 7.71 6.40 6.59 6.39 6.26 6.16 6.09 6.04 6.00
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80.
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
30 4.17 .3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
Table: Values of F at The 1% Significance Level
DoF-denominator
DoF- numerator
1 2 3 4 5 6 7 8 9
1 4052 5000 5403 5625 5764 5859 5928 5982 6022
2 98.50 99.90 99.20 99.20 99.30 99.30 99.40 99.40 99.40
3 34.10 30.80 29.50 28.70 28.20 27.09 27.70 27.50 27.30
4 21.20 18.00 16.70 16.00 15.50 15.20 15.00 14.80 14.70
6 13.70 10.90 9.78 9.15 8.75 8.47 8.26 8.10 7.98
8 11.30 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91
10 10.00 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39
14 8.86 6.51 5.56 5.04 4.70 4.46 4.28 4.14 4.03
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72
5
Table value of ?t? at different degrees of freedom on P=0.05 and 0.01 level
V
P
0.05 0.01
1 6.314 31.821
2 2.920 6.965
3 2.353 4.541
4 2.132 3.747
5 2.015 3.365
6 1.943 3.143
7 1.895 2.998
8 1.860 2.896
9 1.833 2.821
10 1.812 2.764
11 1.796 2.718
12 1.782 2.681
13 1.771 2.650
14 1.761 2.624
15 1.753 2.602
16 1.746 2.583
17 1.740 2.567
18 1.734 2.552
19 1.729 2.541
20 1.725 2.528
21 1.721 2.518
22 1.717 2.508
23 1.714 2.500
24 1.711 2.492
25 1.708 .2.485
26 1.706 2.479
27 1.703 2.463
28 1.701 2.467
29 1.699 2.462
30 1.697 2.457
40 1.684 2.423
60 1.671 2.390
120 1.658 2.338
6
Table: Distribution of chi square corresponding to different levels of significance
Degree of freedom(df)
Probability (P)
0.05 0.01 0.001
1 3.84 6.64 10.83
2 5.99 9.21 13.82
3 7.82 11.35 16.27
4 9.49 13.29 18.47
5 11.07 15.09 20.52
6 12.59 16.81 22.46
7 14.07 18.48 24.32
8 15.51 20.09 26.13
9 16.92 21.67 27.88
10 18.31 23.21 29.59
11 19.68 24.73 31.26
12 21.03 26.22 32.91
13 22.36 27.69 34.53
14 23.69 29.14 36.12
15 25.00 30.58 37.70
16 26.30 32.00 39.25
17 27.59 33.41 40.79
18 28.87 34.81 42.31
19 30.14 36.19 43.82
20 31.41 37.57 45.32
21 32.67 38.93 46.80
22 33.92 40.29 48.27
23 35.17 41.64 49.73
24 36.42 42.98 51.18
25 37.65 44.31 52.62
26 38.89 45.64 54.05
27 40.11 46.96 55.48
28 41.34 48.28 56.89
29 42.56 49.59 58.30
30 43.77 50.89 59.70
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This post was last modified on 20 February 2020