AST-01 Statistical Techniques in English Solved Assignment 2019

AST-01 Statistical Techniques

Course Code: AST-01
Assignment Code: AST-01/TMA/2019
Maximum Marks: 100

AST-01, AST-1, AST 01, AST 1, AST01, AST

1) a) A bag contains 10 white and 3 black balls. Balls are drawn one by one without
replacement till all the black balls are drawn. Find the probability that this
procedure come to an end at the 6th draw. (4)
b) From the list of 500 names and addresses, 100 names are selected without
replacement and 25 wrong addresses were found. Identify the population and
estimate the total no. of addresses needing correction in the list. Also estimate the
standard error of the estimate. (4)

c) A sample of size 3 is to be selected from a population of 10 households. List all
possible samples by linear systematic sampling. (2)

2) a) The mean and the standard deviation of 20 items is found to be 10 and 2
respectively. At the time of checking it was found that one items with value 8 was
incorrect. Calculate the mean and standard deviation if the wrong item is
omitted. (3)
b) A random sample of size 64 has been drawn from a population with standard
deviation 20. The mean of the sample is 80.
i) Calculate 95% confidence limits for the population mean.
ii) How does the width of the confidence interval changes if the sample size is
256 instead? (5)
c) A normal population has a mean of 0.1 and standard deviation 2.1. Find the
probability that the mean of a sample of size 900 will be negative. (2)

3) a) Refills of cartons with apple juice is taking place in a plant. Data for 14 days were
collected and 100 cartons were checked every day for proper filling. Data is as
given below. Compute the UCL, LCL and CL using an appropriate control chart.
Also draw the chart. (5)
S.NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Date 16 17 18 19 20 21 22 23 24 25 26 27 29 30 Total
X 8 2 4 1 3 3 2 4 9 7 5 8 5 9 70
b) For the following series of observations, calculate the 4 yearly centred moving
averages: (5)

Year: 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Annual
Sales
(Rs.
Crores)
2 6 1
4

Can you conclude from the above, the higher the level of education,
the greater is the degree of adjustment in marriage? Justify. (6)
b) Out of 25 newborn babies of obese women, 10 weigh less than 2.5 kg. Find a 95%
confidence interval for the probability that the weight of a newborn baby of an
obese woman is less than 2.5 kg. (4)

5) a) In a partially destroyed laboratory, record of an analysis of correlation of data,
only the following results are legible:
Variance of X = 9
Regression equations are
(i) 8x −10y + 66 = 0
(ii) 0 40x −18y − 214 =
Find out the following missing results.
(i) The means of X and Y
(ii) The coefficient of correlation between x and y
(iii) The standard deviation of Y (5)
b) A random sample of 10 males from a normal population showed a mean height 66
inches and the sum of squares from this mean is equal to 90 sq inches. Is it
reasonable to believe that the average height is greater than 64 inches? Justify
your answer. (5)
6) a) A company is manufacturing cotton threads under different speeds of spindle. The
tensile strength of the thread is a parameter that is of interest to the customer. Data
on different speeds of spindle and corresponding tensile strength on 5 samples is
given. Perform ANOVA to find out which is the most suitable speed for the
spindle so as to have maximum tensile strength. (5)

Speed Tensile strength
1 2 3 4 5
10 22.2 20.6 21.5 20.6 22.0
20 24.2 25.0 24.8 20.7 21.0
30 25.0 23.2 21.7 22.5 20.9
b) The following data were obtained from two random samples. Test whether the
samples come from the same normal population at 5% level of significance.

No. Size Mean Sum of squares of deviation
from mean
1 10 15 90
2 12 14 108
7) a) The following table gives the yield of a hybrid variety of wheat, in quintals per
acre from 17 trial plots of land treated with four types of fertilizers
Marriage Adjustment Score
Level of
Education
Low High Very High
Middle School 25 5 10
High School 50 30 40
College 120 60 60
5

Estimate the number of orchards in the district. (7)
b) The chances that a visit to a primary health centre (PHC) results in neither lab
work, nor referred to a specialist is 35%. Out of those coming to a PHC, 30% are
referred to a specialist, and 40% require lab work. Find the probability that a visit
to a PHC results in both lab work and referral to a specialist. (3)
8) a) Consider a random sample (WOR) of two households from a population of
households having monthly income (in Rs.) as follows: (5)

Enumerate all possible samples (WOR) of size 2 and show that the sample mean
gives an unbiased estimate of population mean.
b) The probability of individuals with blood types A, B, AB and O are 0.45, 0.13,
0.06 and 0.36, respectively. A geneticist tested 100 individual blood types and
found that 40 had type A, 18 had type B, 5 had type AB and 37 had type O. Use
goodness of fit test at 5% level of significance to test whether the observed
frequencies closely correspond to the theoretical ones. (5)
9) a) Plot the following data about demand for an item. Find the moving averages by
taking n = 3. Use these to forecast next two months’ demand. (5)

Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand 46 56 54 43 57 56 67 62 50 56 47 56
b) Previous studies on some spherical seeds have revealed that their mean diameter
is 10 mm with a standard deviation of 2 mm. We start with 1000 seeds and pass
them through two sieves so that only seeds whose diameter is between 9.5mm and
10.5mm are left. Find out the following:
(i) How many such seeds will we get?
(ii) If we discard only those seeds with diameter less than 6 mm, then how many
will be left? (5)
10) Which of the following statements are true and which are false? Justify. (10)
a) The area under the curve of a standard normal distribution between − ∞ and 0 is
0.45.
b) If the probability of being left-handed is 0.1, the probability that none of the 3
persons selected randomly is left-handed is 0.729.
c) If the correlation coefficient is zero, then the relationship between Y and X is
positively linear.
Treatment with fertilizer
A B C D
24 31 39 38
39 25 41 32
35 26 33 35
21 40 34
45 26
Household 1 2 3 4 5
Income 1000 1200 900 1500 1300
6
d) Number of samples chosen by SRSWOR and SRSWR are same if population size
is 6 and sample size is 2.
e) The moving average method used in forecasting uses weighted averages.