Confidence interval in minitab express 2 samples

Confidence interval in minitab express 2 samples free#

Note: For some statistical tests used later in this book, the degrees of freedom are not equal to nВ в€’ 1. The degrees of freedom for a confidence interval for the mean are found by subtracting 1 from the sample size. Hence, the degrees of freedom are 5 в€’ 1 = 4, and this value tells the researcher which tВ curve to use. But once 4 values are selected, the fifth value must be a specific number to get a sum of 50, since 50 Г· 5 = 10.

Confidence interval in minitab express 2 samples free#

The degrees of freedomВ are the number of values that are free to vary after a sample statistic has been computed, and they tell the researcher which specific curve to use when a distribution consists of a family of curves.ДЇor example, if the mean of 5 values is 10, then 4 of the 5 values are free to vary. Many statistical distributions use the concept of degrees of freedom, and the formulas for finding the degrees of freedom vary for different statistical tests. See Figure 7вЂ“6.FIGUREВ 7вЂ“6The tВ Family of Curves

As the sample size increases, the tВ distribution approaches the standard normal distribution.

The tВ distribution is actually a family of curves based on the concept of degrees of freedom,В which is related to sample size.

The tВ distribution differs from the standard normal distribution in the following ways:

The curve approaches but never touches the xВ axis.

The mean, median, and mode are equal to 0 and are located at the center of the distribution.

The tВ distribution is similar to the standard normal distribution in these ways: The tВ distribution shares some characteristics of the standard normal distribution and differs from it in others. Some important characteristics of the tВ distribution are described now. To use this method, the samples must be simple random samples, and the population from which the samples were taken must be normally or approximately normally distributed, or the sample size must be 30 or more.

These values are taken from the StudentвЂ™s t distribution,В most often called the t distribution. When sВ is used, especially when the sample size is small, critical values greater than the values for z О±/2В are used in confidence intervals in order to keep the interval at a given confidence level, such as 95%. However, most of the time, the value of ПѓВ is not known, so it must be estimated by using s, namely, the standard deviation of the sample.

When ПѓВ is known and the sample size is 30 or more, or the population is normally distributed if the sample size is less than 30, the confidence interval for the mean can be found by using the zВ distribution, as shown in Section 7вЂ“1. Today i will teach you about Confidence Intervals for the Mean When Пѓ Is Unknown