![]() ![]() Then we compute the difference in the means, In Figure 9 we first store the margin of error in X. Program we can see that the standard deviation value is stored in the ![]() [We might note that by reading through the We found first in Figure 2 and in Figure 4. The standard deviation of the difference of the means.įor this problem we actually type in the two values that ![]() The margin of error is the product of the t-value and The latter being exactly what we found back in Figure 4. Providing exactly the data from the problem we are doing.įigure 7 provides the computed results. Note that the program goes on to do a bit more calculation, but we will notįigure 5 shows the start of running the program CALCVSDF, Lines 15 through 17 display the computed values. Lines 11 through 13 compute the combined variance. In that program lines 5 through 10 prompt the user for the One might consider writing a program such as The computation for the combined standard deviation is not terrible to remember, but it is a pain to type. Problem the standard deviation of the sample means is. Makes the standard deviation of the difference of the means be given by (which is why we used the t-values rather than use z-scores above). Variance of the populations we use the variance of the samples Is the sum of the variances of the two means. The variance of the difference of the two means 9974997809 of the area to its left, not the asked for Note that the program also give us the fact that Not quite as good as the better and faster built-in routine, but In Figure 2 we start the program, giving the required values.įigure 3 shows the rest of the program output. This will give approximately the same answer. The calculator producesįor those having a calculator without the invT( option, 9975) forĪnd for the given degrees of freedom. T-value having the specified area (for us. The fact that we want 99.5% inside the confidence interval, leavingĠ.5% outside, and that has to be split, half above and have below. The command that we want is invT(.9975,41) where the. On a TI-84 (with the newer operating system) we have the invT( Our first step is to determine the t-value to use for a 99.5% confidence By using the "simple method" our final result willīe a broader confidence interval, one that will most certainly cover the more compact one found later. Of freedom translate into smaller t-values which in turn yield smaller margins of error which result in It is certainly the case that the more complex method, shown later, will give a "higher" degrees of freedom. We use this as the "simple method" for determining the number of degrees of freedom. We are going to create a confidence interval given by We are given the following sample statistics: We want to construct a 99.5% confidence interval for the difference between two sample means from independent samples. Given the actual data values for the two samples Find the confidence interval for the difference of the means Find the confidence interval for the difference of the means for paired data values.Given the statistices of sample size and proportions Find the confidence interval for the difference of proportions.Given the actual data values for the two samples Given the statistics of sample size, mean and standard deviation Find the confidence interval for the difference of the means.We have a number of different instances to examine: This page will examine and step through multiple solutions Some images on this page have been generated via AsciiMathML.js. Return to the Main Math 160 Topics page Revised November, 2012 Confidence Intervals for Two Samples Confidence Intervals for Two Samples
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