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The values for t α/2 are found in Table F in Appendix A. The formula for finding the confidence interval using the t distribution has a critical value t α/2. Note: For some statistical tests used later in this book, the degrees of freedom are not equal to n − 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 − 1 = 4, and this value tells the researcher which t 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 ÷ 5 = 10.
How to do one mean confidence intervals on minitab 18 free#
The degrees of freedom 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.įor 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 7–6.FIGURE 7–6The t Family of Curves As the sample size increases, the t distribution approaches the standard normal distribution.The t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.The t distribution differs from the standard normal distribution in the following ways: The curve approaches but never touches the x axis.The mean, median, and mode are equal to 0 and are located at the center of the distribution.The t distribution is similar to the standard normal distribution in these ways:
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The t distribution shares some characteristics of the standard normal distribution and differs from it in others. Some important characteristics of the t 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 Student’s t distribution, most often called the t distribution. When s is used, especially when the sample size is small, critical values greater than the values for z α/2 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 σ is not known, so it must be estimated by using s, namely, the standard deviation of the sample. When σ 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 z distribution, as shown in Section 7–1. Today i will teach you about Confidence Intervals for the Mean When σ Is Unknown