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

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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 , 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 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.

Use sampling distribution properties to identify the correct option.

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.

Answer only

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

V(x)

(n-1)

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