# MST-005 Solved Assignment 2021

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## MST-005 Solved Assignment 2021

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## MST-005 Solved Assignment 2021

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## (Statistical Techniques)

MST-005: Statistical Techniques

1. State whether the following statements are true or false and also give the reason in support of your answer:
1. Vopt(x̅st) lies between Vprop(x̅st ) and VRandom (x̅st).
2. In cluster sampling, the variance within clusters is greater than the variance between clusters.
3. While analysing the data of a 5 × 5 Latin Square design the error d.f.is equal to 12.
4. In a Two way analysis of variance with 4 blocks & 4 treatments, the degree of freedom for the total variation is 15.
5. Suppose a random number generated by Middle. Square Method is 16, then the next random number will be 44.

2(a) Explain by considering a sample of size n = 2 from a population consisting of five members 2, 3, 6, 8, 11 that SRSWOR gives a better estimator of a population mean that SRSWR.

(b) From the following data find mean and variance of the stratified sampling under

(i) proportional and (ii) Neyman Allocation

 Strata Ni ni Si y̅i 1 2 3 80 160 260 29 39 32 12 8 4 80 30 10 500 100

3(a) In a population of size N = 5, the values of the population characteristics are 1, 3, 5, 7, 9, a sample of size 2 is drawn.

Verify that y̅ is an unbiased estimate of Y̅ and V(y̅ )  is equal to V(y̅ )$$=\frac{N-n\:}{N.n\:}S^2.$$

(b) In order to compare the mileage yields of 3 kinds of gasoline, several tests were run and the following results were obtained:

 Gasoline A: 19 21 20 18 21 21 Gasoline B: 23 20 22 20 24 23 Gasoline C: 20 17 21 19 20 17

Carry out the analysis of variance test and test whether the observed differences between the means of 3 kinds of gasoline may be attributed to chance at 5% level of significance.

1. A manurial trial with six levels of Farm Yard. Manure (FYM) was carried out in a randomised block design with 4 replications at the experimental station Junagarh with a new study the rate of decomposition of organic matters in soil and its synthetic capacity in soil on cotton crop. The yield per plot in kg for different levels of FYM and replications is given below:

Cotton Yield Per Plot (in Kg)

 Levels of FYM Replications I II III IV 1 2 3 4 5 6 6.90 6.48 6.52 6.90 6.00 7.90 4.60 5.57 7.60 6.65 6.18 7.57 4.40 4.28 5.30 6.75 6.50 6.80 4.81 4.45 5.30 7.75 5.50 6.62

Carry out the Analysis of variance test and draw the conclusions.

1. In the following data two values are missing. Estimate these values and analyze the design given as:
 Treatment Block I II III A 12 14 12 B 10 Y 8 C X 15 10

1. The following data is the data pertaining to a feeding trial on sheep. Treatments

A: Grazing only

B: Grazing + Maize Supplements

C: Grazing + Maize + Protein Supplement P1

D: Grazing + Maize + Protein Supplement P2

E: Grazing + Maize + Protein Supplement P3

Layout and Wool Yield (100 gm) is given as:

 32(D) 33(E) 30(C) 28(B) 24(A) 51(C) 45(D) 41(A) 45(E) 29 (B) 41 (E) 29 (A) 24 (B) 36 (D) 35 (C) 38 (B) 39(C) 42(E) 23(A) 37(D) 38(A) 24(B) 21(D) 29(C) 26(E)

1. Analyse the design with appropriate method and calculate the CD for the treatment mean yield.
2. Calculate the relative efficiencies of the above L.S.D over R.B.D and C.R.D.

1. For a factorial experiment with 3 factors, N, P and M each at two levels, the design and yield per plot are given below. Analyse the experiment.
 np 48.81 nm 58.88 pm 46.11 (1) 38.62 m 40.49 p 32.75 npm 61.55 n 55.07 np 50.43 pm 52.31 (1) 40.26 nm 49.62 m 32.36 p 51.94 npm 48.89 n 53.86 n 47.37 npm 46.87 p 37.25 m 46.94 pm 39.30 (1) 39.23 nm 49.93 np 51.43

8(a) Times between successive crashes of a computer system were generated for a 6-months period and are given in increasing order as follows (time in hours):

1, 10, 20, 30, 40, 52, 63, 70, 80, 90, 100, 102, 130, 140, 190, 210, 266, 310, 530,590, 640, 1340.

The value of parameter α and Mean (1/α) is given as 0.00435 and 230 hrs, respectively.

Use kolmogrov-Smirnov test to examine the goodness of fit of exponential distribution.

(b) Generate ten uniform random numbers U(0, 1) from the multiplicative  LCG given below:   xi = (5xi1)mod32 with x0 =1

Also obtain a sequence of heads and tails using above generated random numbers.

Insert math as
$${}$$