ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A A company used three different methods to train its employees. The number of units of output produced by different employees trained by the three training methods are given below: Method A: 50, 45, 55, 44Method B: 64, 48, 52, 56, 44Method C: 46, 42, 48, 45, 57, 42 The estimate of the population variance within the samples for the different methods is: (a) 25.67 (b) 31.07 (c) 38.646 (d) 39.097

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION A company used three different methods to train its employees. The number of units of output produced by different employees trained by the three training methods are given below: Method A: 50, 45, 55, 44 Method B: 64, 48, 52, 56, 44 Method C: 46, 42, 48, 45, 57, 42 The estimate of the population variance on the basis of the variance among the sample means for the above methods is:

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

Which of the following statements are correct in order to obtain the hypothesis H0:β1=0H_0: \beta_1 = 0H0​:β1​=0 for the modelyi=β0+β1xi+εiy_i = \beta_0 + \beta_1 x_i + \varepsilon_iyi​=β0​+β1​xi​+εi​ ?

For a simple linear regression modely=β0+β1x+εy = \beta_0 + \beta_1 x + \varepsilony=β0​+β1​x+ε,consider the following statements where β^0\hat{\beta}_0β^​0​ and β^1\hat{\beta}_1β^​1​ are estimates of β0\beta_0β0​ and β1\beta_1β1​:

Which of the following statements are correct about the generalized inverse of a matrix A? A generalized inverse of a matrix is defined as A A⁻ A = A A generalized inverse is not unique. A matrix to have a generalized inverse must be non-singular. A matrix to have a generalized inverse may be either a square matrix or a rectangular matrix. Select the correct answer using the code given below:

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A Random Effects Model Question (ISS Level) Question Suppose b₁, b₂, b₃, …, bₙ are independent N(0, σ²) random variables and eᵢⱼ are independent N(0, τ²) random variables for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Suppose we observe only: Xᵢⱼ = bᵢ + eᵢⱼ for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Then which of the following assertions are true? Var(Xᵢⱼ) = σ² + τ² for all i, j Cov(Xᵢ

In the Gauss-Markov linear model, letŷ denote the vector of fitted values andê denote the vector of residuals. Consider the following statements: The components of ŷ are pairwise uncorrelated. The components of ê are pairwise uncorrelated.

ISS PREVIOUS YEAR PAPER-1 2016 SOLUTION. The following data pertain to a test involving analysis of variance: Estimate of population variance based on variance among the sample means = 18.50. Estimate of the population variance based on the variance within the samples = 12.50 The F-ratio for the sample is equal to: Options:(a) 0.68(b) 1.48(c) 6.00(d) 31.00

A certain task can be accomplished in a factory by four different workers on five different types of machines. A sample study in context of a two-way design without repeated value is being made with two fold objectives of examining whether the four workers differ with respect to mean productivity and whether it is same for five machines. The researcher involved in this study reports gathered data as under : Sum of squares for variance between machines = 35.2 Sum of squares

Let y = (y1, y2, …, yn)' be the vector of these variables. Suppose y' A y is a quadratic form where A is an idempotent matrix. What will be the distribution of y' A y?

iss previous year solution paper-2 q.no.1