AST-01 Statistical Techniques
Indira Gandhi National Open University
Tutor Marked Assignment
Programme Code: BDP/B.Sc/BA/B.Com
Course Code: AST-01
Assignment Code: AST-01/TMA/2019
|Program||BA/B.Com/B.Sc/BDP (Bachelor’s Degree Programme)|
|Valid||From 1st January 2019 to 31st December 2019|
||PDF Assignment Solution|
|Submission Date||before March 31st, 2019 for the session July, 2018 and
before September 30th, 2019 for the session January 2019
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.
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.
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) 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.
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?
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.
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.
S.NO. 1 2 3 4 5 6 7 8 9 1011 12 13 14
Date 16 17 18 1920 21222324 2526 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:
Year: 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Annual Sales (Rs. Crores) 2 6 1 5 3 7 2 6 4 8 3
4) a) The following table gives for a sample of married women, the level of education and marriage adjustment score:
Marriage Adjustment Score Level of Education Low High Very HighMiddle School25 5 10 High School 50 30 40 College 120 60 60
Can you conclude from the above, the higher the level of education, the greater is the degree of adjustment in marriage? Justify.
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.
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
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
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.
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.
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 MeanSum 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
Treatment with fertilizer A B C D 24 31 39 38 39 25 41 32 35 26 33 35 21 40 34 45 26
Estimate the number of orchards in the district.
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.
8) a) Consider a random sample (WOR) of two households from a population of households having monthly income (in Rs.) as follows:
Household 1 2 3 4 5
Income 1000 1200 900 1500 1300
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.
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.
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?
10) Which of the following statements are true and which are false? Justify.
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.
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.