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IGNOU AST-01
- Statistical techniques,
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(January 2023 - December 2023)

AST-01 Assignment

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IGNOU AST-01 January 2023 - December 2023 - Solved Assignment

Are you looking to download a PDF soft copy of the Solved Assignment AST-01 - Statistical techniques? Then GullyBaba is the right place for you. We have the Assignment available in English language.

This particular Assignment references the syllabus chosen for the subject of Mathematics, for the January 2023 - December 2023 session. The code for the assignment is AST-01 and it is often used by students who are enrolled in the BA, B.COM, B.Sc. Degree.

Once students have paid for the Assignment, they can Instantly Download to their PC, Laptop or Mobile Devices in soft copy as a PDF format. After studying the contents of this Assignment, students will have a better grasp of the subject and will be able to prepare for their upcoming tests.

IGNOU AST-01 (January 2023 - December 2023) Assignment Questions

1. a) Find a 99% confidence interval for the percentage of copper content of brass, if a sample of size 9 gives the following data: 65, 65, 64, 63, 65, 63, 66, 62, 63.
Assume a normal population. You may like to use the values given at the end of the question paper.

b) Plot a control chart for the mean of data from 12 samples of size 5 each on the diameter of small cylinders in mm.

2. a) In the past, the standard deviation of weights of 100 gm packages of tea leaves filled by a machine was 0.8 gm. A sample of 20 packages was drawn and its s.d. was found to be 1.0 gm. Assuming normality at 5% level of significance, test the hypothesis that the population s.d. σ = 8.0 against the alternative hypothesis that s.d. σ > 08.0 .

b) Find the correlation coefficient for data with 20 pairs of values of x and y, if it is given that

c) Explain the following terms of quality control with suitable examples:

i) Process Capability
ii) Tolerance

3. a) i) Write the sample space of the experiment of drawing 3 screws from a box of right-handed (R) and left-handed (L) screws.
ii) If event A: At least one R is drawn
event B: At least one L is drawn
event C: Exactly 2 right-handed screws are drawn
event D: Exactly 2 left-handed screws are drawn
Are the events A and B mutually exclusive? Are C and D mutually exclusive? Justify your answer.

b) The sick leave time for workers in a factory is normal with mean 1000 hours and s.d. 100 hours, per month. How much time t should be budgeted next month exceeds the time corresponding to the probability 20%.

c) Find the moving averages of length 3 for the following data. Also, plot these averages.

4. a) Find the mean and variance of the following data:

b) Suppose from a total of 120 guava bearing trees in a village, 5 clusters of 4 trees each are selected and yield (in kg) recorded is a given in the following table:

Estimate the average yield (in kg) per tree of guava using cluster sampling method and simple random sampling method.

5. a) A sample of 6 boxes is to be selected from 30 boxes of mangoes numbered 1 to 30. Find the samples using:
i) Direct WR method
ii) Remainder approach
iii) Quotient approach, stating clearly the starting random numbers chosen by you.

b) Find the regression line of y on x

6. a) A random sample of size 4 is taken from each of 3 independent normal random variables X1, X2, X3 resulting in the following data:

Assuming that the 3 variables have equal variances, test at the 0.05 significance level, the hypothesis that X1, X2, X3 have the same mean using ANOVA. You may like to use following values.

b) Suppose you are waiting at a bus stand for a bus. Every 10 minutes, you are recording the number of buses that pass by you. Data recorded is as follows:

Identify the distribution, the buses follow. Calculate the average number of buses that pass you and the variance.

7. a) In the amount of cosmic radiations to which a person is exposed while flying across a specific continent is a normal random variable with mean 4.35 units and S.D. 0.59 units. Find the probabilities that the amount of exposure during such a flight is (i) between 4.00 and 5.00 units, (ii) at least 5.50 units.

b) A sampling random sample of size 100 has mean 15 and population variance 25. Find an interval estimate of the population mean with a confidence level of 99% and 95%.

c) A hypothetical population consists of the numbers 2, 5 and 7. Write all possible simple random samples of size 2 (with replacement). Verify that the sample mean is an unbiased estimator of the population mean.

8. a) The following random samples are measurements of the heat producing capacity in millions of calories per ton of specimens of coal from mines:

Test at 5% level of significance whether the difference between the means of two samples is significant?

b) A company operates four machines on three separate shifts daily. The following table presents the data for machine break-downs resulted during a 6 month time period:

At 5% level of significance test the hypothesis that for an arbitrary breakdown in the machine causing the breakdown and the shifts are independent.

9. a) The three drying techniques for curing a glue were studied and the following times were observed:

At α = 0.05, test the hypothesis that the average times for three formulae are same

b) The following data represent the number of defects discovered at a factory on 20 successive batches of 10 cars each:

Does it appear that the production process is in statistical control throughout? Give justification.

10. Which of the following statements are true and which are false?

a) If X is continuous random variables following uniform distribution with values in [2, 6] then P (X = 4) = 0
b) A 90% confidence interval calculated using a sample of size 40 is smaller than the one calculated using a sample of size 100.
c) If a dice is rolled twice, then the number of possible outcomes is 36.
d) If every 5th student on the roll is selected and her height is measured, the sampling method used is simple random sampling.
e) A type I error is committed when we fail to reject a null hypothesis when the alternative hypothesis is true.

IGNOU AST-01 (January 2022 - December 2022) Assignment Questions

1. a) The distribution of a discrete random variable X is given as :

Find :
(i) The value of K
(ii) P (X >2)
(iii) E (X)
(iv) Draw a rough sketch of the distribution.
b) For overall quality improvement of cloth, a textile manufacturer decides to monitor the number of defects in each bolt of cloth. The data from 10 inspections is reported as follows :

Draw an appropriate control chart to check whether the process is under statistical control.

2. a) Three dice are rolled. If no two dice show the same number on the top face, what is the probability that one dice shows ‘1’ on the top face?
b) If 2% of the books bound at a certain binary have defective bindings, determine the probability that 5 of 400 books bound by this binary will have defective bindings.
[Given that e-8 = 0.00034]

3. a) Out of 20,000 customers’ leader accounts, a sample of 600 accounts was taken to test the accuracy of posting and balancing wherein 45 mistakes were found. Determine the 95% confidence interval for number of defective cases.
b) In 16 one-hour test runs, the gasoline consumption of an engine on an average is found to be 16⋅ 4 gallons with a standard deviation of 2⋅1 gallons. At 5% level of significance, test the claim that the average gasoline consumption of this engine is 12⋅0 gallons per hour
c) A sample of 100 employees is to be drawn from a population of collages A and B. The population means and population mean squares of their monthly wages are given below:

Determine the sample size to be taken using (i) proportional allocation, and (ii) Neyman allocation methods.

4. a) A company has sales (y) which shows profit on the cost of production (x) of furniture when sold to government agencies. The regression lines are y = x + 5 and 16x = 9y + 95.
Find :
(i) Mean of sale and production cost.
(ii) Correlation coefficient between sales and production cost.
(iii) If σy = 4, find σx.
(iv) Predict the production cost when sale is 2,000.
b) An oil company claims that less than 20% of all the car owners have not tried its oil. Test the claim at the 0⋅01 level of significance if a random check reveals that 22 of 200 car owners not tried its oil.

5. a) The odds that a research monograph will be accepted by 3 independent referees are 3 to 2, 4 to 3 and 2 to 3, respectively. Find the probability that of the three reports :
(i) all will be accepted.
(ii) more than 1 of the reports will be favorable.
b) A company installed 10000 electric bulls in a metro. If these bulbs have an average life of 1000 hours with S. D of 200 hours. Assuming normality, what number of bulls might be expected to fail (i) in the first 800 hours (iii) between 800 and 1200 hours.
c) Cite two situations where systematic sampling is appropriate. Explain, how it is different from stratified sampling. Justify.

6. a) A random sample is selected from each of three types of ropes and their breaking strength (in pounds) are measured with the following results :

Test whether the breaking strength of the ropes differs significantly at 5% level of significance.
b) Works out the 5-yearly moving average for the data of a number of commercial industrial failures in a country during 7985 to 2000:

7. a) A cigarette company interested in the effect of gender on the type of cigarettes smoked and has collected the following data from a random sample of 150 persons :

At 95% level of significance, test whether the type of cigarette smoked and gender are independent.
b) The lifetime (in ‘000 hours) of five LED bulbs of 10 watts are 46, 40 48, 50 and 42. Draw all possible random samples of size 3 without replacement and estimate the average lifetime of the LED bulbs.

8. a) Following frequency distribution presents the lifetimes of 200 incandescent lamps :

Draw the histogram, ‘more than’ and ‘less than’ ogive. Also, find the median from the ogives.
b) Draw all the possible samples of sizes 2 without replacement from the population {8, 12, 20} and verify that the sample mean is the unbiased estimator of population mean. Find the variance of the estimate the population mean.

9. a) Suppose that a testing procedure A results in 20 unacceptable transistors out of 100 produced whereas another testing procedure B results in 12 unacceptable transistors out of 100 produced. Can we conclude at 5% level of significance that the two methods are equivalent?
b) Two different sampling techniques were adopted while investigating the same group of students to find the number of students falling in different intelligence level. The results are tabulated as follows :

At 5% of level of significance, test whether the sampling techniques adopted significantly different ?

10. Which of the following statements are True and False? Justify your answers.
a) If bxy = 0⋅9 and byx = −0⋅9, then r = 0⋅81.
b) If a pair of dice is thrown, then the probability that the sum of the number on the top faces is greater than 12 is 0.
c) If the probability of being left-handed is 0⋅1, then the probability that none of the 3 persons selected randomly is left-handed is 0⋅729.
d) Analysis of variance is a technique to test the equality of variation in several populations.
e) If the level of significance is the same, the area of the rejection in a 2-tailed test is less than in a 1-tailed test.

AST-01 Assignment Details

  • University IGNOU (Indira Gandhi National Open University)
  • Title Statistical techniques
  • Language(s) English
  • Session January 2023 - December 2023
  • Code AST-01
  • Subject Mathematics
  • Degree(s) BA, B.COM, B.Sc.
  • Course Application-Oriented Courses (AOC)
  • Author Gullybaba.com Panel
  • Publisher Gullybaba Publishing House Pvt. Ltd.

Assignment Submission End Date

The IGNOU open learning format requires students to submit study Assignments. Here is the final end date of the submission of this particular assignment according to the university calendar.

  • 30th April (if Enrolled in the June Exams)
  • 31st October (if Enrolled in the December Exams).

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English Language

  • January 2023 - December 2023 37 Pages (0.00 ), PDF Format SKU: IGNGB-AS-BS-AST01-EN-395
  • January 2022 - December 2022 40 Pages (0.00 ), PDF Format SKU: IGNGB-AS-BS-AST01-EN-177

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