Practice Questions on Population Variance
Q1. The population variance is also called:
a) Sigma squared
b) Sigma cubed
c) Sigma
d) None of the above
Q2. When a sample variance of 25 is obtained from a sample of 10 items from a normal population, the 80% confidence interval for a population variance is:
a) 12.3 to 57.1
b) 13.3 and 67.7
c) 14.1 to 46.25
d) 15.3 to 53.98
3. The sampling distribution of the ratio of independent sample variances from two normally distributed populations with equal variances is the:
a) Chi-square distribution
b) Normal distribution
c) F distribution
d) T distribution
4. These sample results were obtained for independent random samples from two normally distributed populations. Sample 1: Sample Size 10, Sample Variance 25. Sample 2: Sample Size 16, Sample Variance 20. Using a .05 level of significance, which conclusion would be reached for these data?
a) There is a statistically significant difference between the variances of the two populations.
b) There is no statistically significant difference between the variances of the two populations.
c) Insufficient data – can’t tell in this case.
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Population Variance
Population variance is a fundamental concept in statistics that quantifies the average squared deviation from the mean of a set of data points in a population. It is a measure of how spread out a group of data points is.
There are two types of data available, namely, ungrouped and grouped data. Thus, there are two formulas to calculate the population variance. In this article, we will learn more about population variance, its formulas, and various associated examples.
Table of Content
- What is Population Variance?
- Formula of Population Variance
- Ungrouped Data
- Grouped Data
- Population Variance and Sample Variance
- Population Variance and Standard Deviation
- Solved Problems on Population Variance
- Practice Questions on Population Variance
- FAQs on Population Variance