In the output, the null and alternative hypotheses help you to verify that you entered the correct value for the hypothesized standard deviation or hypothesized variance.
The sample size (N) is the total number of observations in the sample.
The sample size affects the confidence interval and the power of the test.
Usually, a larger sample size results in a narrower confidence interval. A larger sample size also gives the test more power to detect a difference. For more information, go to What is power?.
The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The symbol σ (sigma) is often used to represent the standard deviation of a population, while s is used to represent the standard deviation of a sample. Variation that is random or natural to a process is often referred to as noise.
The standard deviation uses the same units as the data.
The standard deviation of the sample data is an estimate of the population standard deviation.
Because the standard deviation is based on sample data and not on the entire population, it is unlikely that the sample standard deviation equals the population standard deviation. To better estimate the population standard deviation, use the confidence interval.
The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared.
The variance of the sample data is an estimate of the population variance.
Because the variance is based on sample data and not on the entire population, it is unlikely that the sample variance equals the population variance. To better estimate the population variance, use the confidence interval.
The confidence interval provides a range of likely values for the population standard deviation or the population variance. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population standard deviation or population variance. The percentage of these confidence intervals or bounds that contain the standard deviation or the variance is the confidence level of the interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population standard deviation or the population variance.
An upper bound defines a value that the population standard deviation or population variance is likely to be less than. A lower bound defines a value that the population standard deviation or population variance is likely to be greater than.
The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.
Minitab cannot calculate the Bonett method with summarized data.
 

In these results, the estimate of the population standard deviation for the length of beams is approximately 0.87, and the estimate of the population variance is approximately 0.76. Because the data did not pass a normality test, use the Bonett method. You can be 95% confident that the population standard deviation is between approximately 0.704 and 1.121.
The degrees of freedom (DF) indicate the amount of information that is available in your data to estimate the values of the unknown parameters, and to calculate the variability of these estimates. For a 1 variance test, the degrees of freedom are determined by the number of observations in your sample.
Minitab uses the degrees of freedom to determine the test statistic. The degrees of freedom are determined by the sample size. Increasing your sample size provides more information about the population, which increases the degrees of freedom.
The test statistic is a statistic for chisquare tests that measures the ratio between an observed variance and its hypothesized variance.
You can compare the test statistic to critical values of the chisquare distribution to determine whether to reject the null hypothesis. However, using the pvalue of the test to make the same determination is usually more practical and convenient. The pvalue has the same meaning for any size test, but the same chisquare statistic can indicate opposite conclusions depending on the sample size.
The test statistic is used to calculate the pvalue. Because there is no test statistic for the Bonnet method, Minitab uses the rejection regions that are defined by the confidence limits to calculate a pvalue.
The pvalue is a probability that measures the evidence against the null hypothesis. A smaller pvalue provides stronger evidence against the null hypothesis.
Use the pvalue to determine whether the population variance or population standard deviation is statistically different from the hypothesized variance or standard deviation.
When you have summarized data, Minitab cannot calculate a pvalue for the Bonett method.