ISS Statistics Paper II (Old Subjective Pattern): Questions 9 - 13 of 39

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Question number: 9

» Hypotheses Testing » Randomised Test

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Bring out the difference between a randomized and non-randomized test. Explain how the decision based on a randomized test can be taken in the discrete set-up.

Explanation

A test T of a hypothesis H is said to be non-randomized test if the decision about the rejection or acceptance of H is based on a test statistic. H is rejected if the test statistic lies in the critical region otherwise accepted. A randomized test is one in which… (87 more words) …

Question number: 10

» Linear Models » Analysis of One-Way Classified Data » Mixed Model

Appeared in Year: 2014

Essay Question▾

Describe in Detail

A manufacturer of television sets is interested in the effect on tube conductivity of five different types of coating for color picture tubes. Sample means are

y1.=49,y2.=51,y3.=53,y4.=57,y5.=58

Error sum of squares = 54.0

(i) Is there a difference in conductivity due to coating type? F-value = 3.09

(ii) Determine which pair differs significantly using Bonferroni t-interval. Comment on the same.

(t15(0.0520)=3.286)

Explanation

(i)

Test the null and alternative hypothesis is

H 0 : There is no difference in the means of conductivity due to coaching type:

μ1=μ2=μ3=μ4=μ5

H 1 : At least one mean is different from others.

Assume… (285 more words) …

Question number: 11

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Let X~N3(0,Σ) , Σ=(1ρ0ρ1ρ0ρ1)

Find ρ such that X 1 +X 2 +X 3 and X 1 -X 2 -X 3 are independent.

Explanation

Let

Y=X1+X2+X3=(111)(X1X2X3)=AX

Z=X1X2X3=(111)(X1X… (101 more words) …

Question number: 12

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Show that Z=16(X1+2X2+3X3) is not a sufficient estimator of the Bernoulli parameter θ.

Explanation

Let X i is a ith random variable follows Bernoulli distribution with parameter θ. Then, the random variable is defined as

Xi=(1,withprobabilityθ0,withp… (195 more words) …

Question number: 13

» Statistical Quality Control » Control Charts » Attributes

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Find 3-sigma control limits for a

(i) C-chart with process average equal to 4 non-conformities

(ii) U chart with process average c = 4, and n = 4.

Explanation

the 3-sigma control limits is

(i) Given that c=4

Control limits for the C chart with a known non-conformities is

U.C.L.=c+3c=4+3×2=10

C.L.=c… (90 more words) …

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