Past Papers Biostatistics

By: Prof. Fazal Rehman Shamil

Guess Paper 1: Biostatistics Fall – 2020 Past Papers

University Name – Confidential

NOTE: Q.1 is compulsory, attempt any four questions from the remaining. All questions carry equal marks. Phones and other Electronic Gadgets are not allowed.

Time Allowed: 3 hours

Total Marks:    70, Passing Marks (35)

Q No.1) Mark the following statement as true or false.
i. Bio-statistics is a collection of statistical tools and techniques that are used to convert data into meaningful information in the field of medical and health/biological sciences.
ii. For any distribution, the sum of the deviations taken from the mean always equals to zero.
iii. A relative measure of dispersion is one that measures the dispersion in terms of the same units or in the square of units, as the units of the data.
iv. The difference between the largest and the smallest observation in a set of data is called Range.
v. Probability ranges from -1 to +1.
vi. P and n are the two parameters of normal distribution.
vii. For a Poisson distribution, mean and variance are always equal.

Q No.2) a) The weights of 50 football players are listed below:
193 240 217 283 268 212 251 263 275 208
230 288 259 225 252 236 243 247 280 234
250 236 277 218 245 268 231 269 224 259
258 231 255 228 202 245 246 271 249 255
265 235 243 219 255 245 238 257 254 284

Make a grouped frequency distribution for the above data, taking 10 units as the width of class interval. Indicate class limits and class boundaries clearly.
b) Construct the Histogram for the following frequency distribution relating to the ages of telephone operators.

Age (Years) 20—24 25—29 30—34 35—39 40—44 45—49
No. of Operators 10 15 22 30 25 20

Q No.3) The given data is subset of the data from a study on a series of male patients admitted in a hospital of large city, after heart attack. The variable of interest is the time in month from when patient was admitted until outcome
14, 16, 40, 9, 42, 5, 18, 23, 72, 3, 42, 76, 53, 38, 65
Find (i) the arithmetic mean, (ii) the geometric mean, (iii) the median and (iv) the mode

Q No.4) Find (i) the range (ii) the mean deviation from mean and (iii) the standard deviation of period in days of incubation of TB patients, when data was found to be as
22, 26, 30, 32, 24, 22, 28, 24, 30, 28, 22, 29

Q No.5) a) In a locality 40% population has “O+” blood group, a sample of 10 persons is taken for blood donation, what is the probability that exactly 4 persons have blood group “O+”.
b) The probability that a person will die from a certain respiratory infection is 0.002, find the probability that 5 of next 2000 so infected will die.

Q No.6) Suppose that weights of 1000 students are normally distributed with mean 150 pounds and standard deviation 25 pounds. Find the number of students with weights (i) less than or equal to 100 pounds, (ii) between 110 and 140 pounds, (iii) between 160 and 180 pounds, (iv) greater than or equal to 190 pounds.

Q No.7) A finite population consists of the numbers 1, 3, 5 and 7.
(i) Form the sampling distribution of , when random samples of size 2 are drawn, with replacement.
(ii) Verify that .

Q No.8) Define the following:
a. Biostatistics
b. Primary Data & Secondary Data
c. Classification & Aims of Classification
d. Regression & Correlation
e. Classical definition of Probability

Guess Paper 2: Biostatistics Spring- 2020 Past Papers

University Name – Confidential

NOTE: Q.1 is compulsory, attempt any four questions from the remaining. All questions carry equal marks. Phones and other Electronic Gadgets are not allowed.

Time Allowed: 3 hours

Total Marks:    70, Passing Marks (35)

Q No.1) Write “True” and “False” for the statements given below:
1. Sample is the small part of population which represents the whole population.
2. Data that have been originally collected and have not undergone any sort of statistical treatment, are called Secondary data.
3. Classification is the sorting of data into homogeneous classes or groups according to their being alike or not.
4. The arithmetic mean is affected by the extreme values.
5. An absolute measure of dispersion is one that measure the dispersion in terms of the same units as the units of the data.
6. A binomial experiment always has three or more possible outcomes to each trial.
7. Stratified random sampling & Systematic random sampling are the techniques of non probability sampling.
Q No.2) a) Tabulate the following marks in grouped frequency distribution, taking 10 units as the width of class interval. Indicate the class limits and class boundaries clearly.
100 96 92 88 86 84 82 80 78 91
87 83 79 77 75 73 71 69 58 56
73 50 57 55 53 51 48 46 63 59
52 69 49 47 45 43 41 58 54 50
56 44 42 40 38 36 46 53 50 43
64 79 48 81 94 66 83 61 55 99
b) Represent the total expenditure and expenditures on various items of a family by a Pie Diagram.
Items: Food Clothing House Rent Fuel & Light Misc.
Expenditure: (in Rs.) 50 30 20 15 35

Q No.3) Calculate the mean, median & mode from the following frequency distribution.
Wages (in Rs.) 30—39 40—49 50—59 60—69 70—79
No. of workers 15 8 16 29 12

Q No.4) It is often stated that in frequency distributions there exists the approximate relation

Test this statement in the following distribution.

Weight
(grams) 65—84 85—104 105—124 125—144 145—164 165—184 185—204
f 9 10 17 10 5 4 5

Q No.5) a) Is there any inconsistency in the following statement?
“The mean of a binomial distribution is 60 and its variance is 36”
If no inconsistency is found, then find the value of
b) The number of accidents in a year attributed to taxi drivers in a city follows Poisson distribution with mean 3. Out of 1,000 taxi drivers, find approximately the number of drivers with no accident in a year.
Q No.6) Time taken by a construction company to construct a flyover is a normal variate with mean,
days and standard deviation of 50 days. What is the probability that:
i) the company takes less than 350 days to complete the flyover
ii) the company takes more than 250 days to complete the flyover
iii) the company takes 250 to 350 days to complete the flyover
Q No.7) A finite population consists of the numbers 3, 5, 7, 9 and 11.
(i) Form the sampling distribution of , when random samples of size 2 are drawn, without replacement.
(ii) Verify that .
Q No.8) Define the following:
1. Descriptive Statistics and Inferential Statistics
2. Primary Data & Secondary Data
3. Properties of Good Average
4. Probability Sampling & Non-Probability Sampling
5. Sampling error & Non-sampling error

Guess Paper 3: Biostatistics Fall – 2019 Past Papers

University Name – Confidential

NOTE: Q.1 is compulsory, attempt any four questions from the remaining. All questions carry equal marks. Phones and other Electronic Gadgets are not allowed.

Time Allowed: 3 hours

Total Marks:    70, Passing Marks (35)

Q No.1)           Write “True” and “False” for the statements given below

  1. Point estimate provides a single value of a statistic that is used to approximate a population

parameter.

  1. A composite hypothesis is one in which all parameters of the distribution are specified.
  • A test for which is small, is called to be a powerful test.
  1. In contingency table, the degree of freedom for chi-square variate is 1.
  2. ANOVA technique is used to test the equality of more than two means.
  3. The co-efficient of correlation “r” always lies between 0 and 1.
  • The parameter in the linear regression model is called regression         co-efficient.

Q No.2)    a)    A random sample of size  from a normal population yielded the sample values Find a 95% confidence interval for

  1. b) In a random sample of 500 homes in a certain city, it is found that 325 are heated by natural gas. Find 90% confidence interval for the fraction of homes in this city that are heated by natural gas.

 

Q No. 3)   a)    Describe the general procedure for testing of hypothesis?

  1. b)   A sample of size 50 from a non-normal population yielded the sample mean  and  . Test against  using a 0.05 significance level.

 

Q No. 4)          The scores of two groups A & B are given below

                                    Group A: 12, 13, 16, 14, 15, 12, 15, 14, 13 and 16.

                                    Group B: 10, 13, 14, 12, 15, 16, 12, 14 and 11.

                        Assumed that the scores are normally distributed & the standard deviation for each group is unknown but identical. Determine whether the means of the two groups differ significantly at 0.05 level of significance.

Q No.5)           Test the null hypothesis that the two variables of classification are independent, using a 0.05 level of significance.

Classes  A1                  A2                A3
B1

B2

B3

 56                 51                 93

118                207              375

26                  42                32

 

Q No.6)           Sixteen men are used in an experiment, four being assigned at random to each of the four

                        machines. The observations are the amounts produced by the machines in one day. Test the

hypothesis at that the machines are not different with respect to the number of items         produced.                                                       

Machine Number
1 2 3 4
52

27

53

34

29

36

29

37

53

45

64

60

33

39

43

36

 

Q No.7)           Calculate the co-efficient of correlation between X and Y and interpret it.                          

X  3       4       5       6       7       8       9       10     11      12
Y 25     24     20     20     19     17     16      13     10       6

 

Q No.8)           Compute the least squares regression line of Y on X for the following data.

X   5        6          8         10         12
Y  16      19        23        28         36
  1. What is the regression co-efficient and what does it mean?
  2. Find the predicted values of Y for X= 15 & 20.

Guess Paper 4: Biostatistics Fall – 2018 Past Papers

University Name – Confidential

NOTE: Q.1 is compulsory, attempt any four questions from the remaining. All questions carry equal marks. Phones and other Electronic Gadgets are not allowed.

Time Allowed: 3 hours

Total Marks:    70, Passing Marks (35)

Q.1      Write “True” and “False” for the statements given below

  1. Estimation is a procedure by which we obtain an estimate of the true but unknown value of a population parameter by using the sample observations.
  2. The sample variance is point estimator of the population variance
  • A simple hypothesis is one in which all parameters of the distribution are not specified.
  1. A test for which is small, is called to be a powerful test.
  2. In simple linear regression model, the regression co-efficient shows change in Y due to unit change in X.
  3. The co-efficient of correlation “r” always lies between -1 and 1.
  • To test the equality of more than two means, we use Analysis of Variance technique.

Q.2    a)           A random sample of 50 chocolate bars of a certain brand hascalories and  calories. Construct the 95% confidence interval for the true mean calories contents of this brand of energy. Assume that the distribution of calories is normal.

  1. b) Constipation was considered a common featured as observed in typhoid. In a sample of 500 typhoid cases, 150 had constipation. Find 90% confidence interval for the proportion of constipation in population.

Q.3   a)            The IQ’s of the college students are known to be normally distributed with a mean of 123. A random sample of 49 students showed an average IQ of and. Test the hypothesis that  against. Let

  1. b) A basket ball player has hit on 60% of his shots from the floor. If on the next 100 shots he makes 70 baskets, would you say that his shooting has improves? Use a 0.1 level of significance.

Q.4                  Thirteen persons were divided at random in two groups, the members of first group were given one kind of drug (called B), and the second group was given another drug (called G), blood is to be taken from each person and time it takes the blood to clot is to be recorded.

Drug B 8.8, 8.4, 7.9, 8.7, 9.1, 9.6
Drug G 9.9, 9.0, 11.0, 9.6, 8.7, 10.4, 9.5

Test against. Let Assuming that population standard deviations are unknown but identical.

                       

Q.5  According to the medical research it is said that crinkles around the eyes are due to smoking. A sample of 500 people was taken. Habits of smoking and crinkles around the eye were observed, following the data is given:

 

Classes Crinkles Not-Crinkles Total
Smoking

Not-smoking

95

105

55

245

150

350

Total 200 300 500

Whether this data shows any relationship between smoking habits and crinkles. Let .

Q.6                  Fasting samples of blood are taken from three individuals for estimation of blood sugar. Their blood sugar at different points are taken as below                          

A B C
70

76

73

75

70

85

79

82

80

83

75

80

76

78

79

 

                        Perform an ANOVA and interpret result. Let

Q.7                  Below is the data of 7 patients. The “X” variable indicates the length of stay at hospital and “Y” shows the average cost in thousands of the stay in hospital. Find the coefficient of correlation between X and Y for the data given below:                         

X (days) 2 4 5 6 8 11
Y (average cost) 18 12 10 8 7 5

 

Q.8                  An aptitude test score (X) of applicants and a measure of productivity (Y) are examined by a management and the data recorded is given in the following table:

X 20 19 17 23 20
Y 29 33 35 32 38

 

Estimate the regression line of Y on X and Show that

Prof. Fazal Rehman Shamil