ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 145 - 150 of 165

Let X ₁, X ₂, …, X _n and Y ₁, Y ₂, …, Y _n are samples variables and the correlation coefficient of between this paired samples is denoted by r. If X’s and Y’s are follows independent normal random variables and correlation coefficient is ρ. Then, we test the null hypothesis is that the relationship of random variable X and Y is not linear and the a

In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation.

Suppose a value of X _i has n _i values of Y say, Y _i1, Y _i

The probability generating function is defined as

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 8 and sample 2 is Y variables of size m = 9 from two population F ₁ (x) and F ₂ (y) respectively.

The hypothesis under the test is that the null hypothesis is the two population are identical otherwise the alternative is the population is differ.

First we find the regression coefficient β _YX where Y is the price at Mumbai and X is the price at Kolkata.

where ρ=0.8, σ _Y =3.5, σ _X =2.5

The estimated regression equation of Y corresponding to X is

where

Rs. 72.6 are the most likely price in Mumbai cor

The cumulative frequency is

Median is 46 which lies in the class 40 - 50. So, median class is 40 - 50.

Here n = 229, l = lower limit of median class = 40

cf = cumulative frequency of the above median c