Which of the following is not a property of the sampling distribution of the variance?

Which of the following is NOT a property of the sampling distribution of the​ variance? Choose the correct answer below. A. The distribution of sample variances tends to be a normal distribution. B. The mean of the sample variances is the population variance. C. The expected value of the sample variance is equal to the population variance. D. The sample variances target the value of the population varianc

Answer

General guidance

Concepts and reason
Variance: Variance is the average of the squared deviation of the random variable from its mean. It represents the spread of the data from the mean. It is denoted by or V(x), where X represents the random variable. Sampling Distribution: Sampling distribution represents the distribution for the statistic for the random sample.

Fundamentals

Properties of sampling distribution of variance: • The sampling distribution of variance is chi square distribution with (n-1) degrees of freedom, n represents the sample size. • The sample variance is the representative of population variance. • The mean of the sample variance is equal to the population variance.

• The sample observations drawn from the normally distributed population.

Step-by-step

Step 1 of 2

The population variance is represented by the sample variance. Moreover, from the sampling distribution of variance properties, the mean (Expected value) of sample variance is equal to the population variance.

The incorrect options are identified by using the properties of sampling distribution for the variance.

Step 2 of 2

The sample variance is the right skewed distribution and moreover, the sample variance follows chi square distribution.

The distribution of sample variance tends to be a normal distribution.


The nature of the distribution is identified by observing the shape of the sampling distribution as right skewed.

Answer

The distribution of sample variance tends to be a normal distribution.

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