Home / Assignment Help / Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances?

Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances?

Answer:

chi square distribution with df = n-1

Step-by-step explanation:

Given that sample of size n=90  are randomly selected from the population of numbers (0 through 9) produced by a random-number generator

Since sample size is large and randomness is followed we can assume that the variable follows a normal distribution.

Hence the sample variance would follow a chi square distribution with degree of freedom = n-1\=89

This is because we have frac{x-mu}{sigma} is standard normal hence square will be a chisquare variate.  When we sum n variates we get chi square distribution with df n-1

About eduhawks

Check Also

Are the phases of the moon the same everywhere on earth

Are the phases of the moon the same everywhere on earth