Assignment III Questions

22CEBS401 – PROBABILITY AND STATISTICS FOR CIVIL ENGINEERING

ASSIGNMENT- III

Part A

1.      What is the concept of bias in the estimation of parameters?

2.      What is MSE (mean square error)?

3.      What is the purpose of two way ANOVA test?

4.      What are ‘confidence intervals’?

5.      Define bias and precision.

6.      What do you mean by parameter?

7.      What is the purpose of one way ANOVA test?

8.      What is meant by sample size?

PART B

1.      Mention the various steps involved in testing of hypothesis.

2.      Mean of the population is 0.700, Mean of the sample is 0.742, Standard deviation of sample 0.040 and sample size is 10. Test the Null Hypothesis for population mean of 0.700.

3.      Briefly explain Completely Randomized Design.

4.      The standard deviation of the life time of a sample of 200 electric light bulbs was computed to be 100 hours. Find the 95% confidence limits for the standard deviation of such electric bulb lights.

5.      List down the properties of estimators with examples.

6.      Explain hypothesis testing concepts.

7.      State the uses of ANOVA test.

8.      List the merits and demerits of random design.

PART C

1.      The mean value of a random sample of 60 items was found to be 145, with a standard deviation of 40. Find the 95% confidence limits for the population mean. What size of the sample is required to estimate the population mean within 5 of its actual value with 95% or more confidence, using the sample mean?

2.       

a)      Give an example of estimators that are

                                                              i.      unbiased and efficient

                                                             ii.      unbiased and inefficient

                                                           iii.      biased and inefficient

b) In a sample of 5 measurements, the diameter of a sphere was recorded by a scientist as 6.33, 6.37, 6.36, 6.32 and 6.37 cms. Determine unbiased and efficient estimates of the true mean and the true variance.

3.       

a)      What is the procedure to conduct ANOVA test for two-way classification?

b)      How do you determine sample size using confidence intervals?

4.      A population consists of 5 numbers 2,3,6,8,11. Consider all possible samples of size 2 that can be drawn with replacement from this population. Find

a)      The mean of the population,

b)      the standard deviation of population,

c)      the mean of the sampling distribution of means and

d)      the standard deviation of the sampling distributions of means.

5.      A population consists of 5,10,14,18,13,24. Consider all possible samples of size two which can be drawn without replacement from the population. Find (a)Mean of the population, (b) Standard Deviation of the population, (c) Mean of the sampling distribution of Means and (d) Standard Deviation of sampling distribution of Means.

6.       

a)      Explain Method of Maximum Likelihood.

b)      State the properties of Maximum likelihood estimators.

7.       

a)      What are the two types of problems encountered in sampling theory?

b)      Experience has shown that 20% of a manufactured product is of top quality. In one day’s production of 400 articles, only 50 are of top quality. Show that either the production of the day chosen was not a representative sample or the hypothesis of 20% was wrong. Based on the day’s production, find also the 95% confidence limits for the percentage of top-quality product.

8.      What is One way and Two-way ANOVA? Give examples of usage of these in real life. Discuss the procedure to perform one-way, two-way ANOVA Tests.

 

 

 

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