Find the t- test for the standard deviation of the two standard deviation numbers. 1. 0.75 2. 1.37

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Find the t- test for the standard deviation of the two standard deviation numbers. 1. 0.75 2. 1.37

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## Answer The t-test is a statistical test that is used to compare the means of two groups to see if they are significantly different from each other. However, you're asking about comparing two standard deviation numbers, which is not typically done with a t-test. If you want to compare the variability of two different groups, you might want to use an F-test instead. The F-test is used to compare the variances of two groups. However, if you insist on using a t-test, you can treat the standard deviations as the means of two groups. Here's how you can do it: ### Step 1: Calculate the Mean The mean (average) of the two standard deviations is: ``` (0.75 + 1.37) / 2 = 1.06 ``` ### Step 2: Calculate the Variance The variance is the average of the squared differences from the Mean. Here's how to calculate it: ``` ((0.75 - 1.06)^2 + (1.37 - 1.06)^2) / 2 = 0.0962 ``` ### Step 3: Calculate the Standard Deviation The standard deviation is the square root of the Variance. So, the standard deviation of the two standard deviations is: ``` sqrt(0.0962) = 0.31 ``` ### Step 4: Calculate the t-score The t-score is calculated as: ``` t = (mean - 0) / (standard deviation / sqrt(n)) ``` Where `n` is the number of observations. In this case, `n` is 2. So, the t-score is: ``` t = (1.06 - 0) / (0.31 / sqrt(2)) = 4.77 ``` So, the t-score for the two standard deviations is 4.77. This is a very high t-score, suggesting that the two standard deviations are significantly different from 0. However, keep in mind that this is not a typical use of the t-test, and the results should be interpreted with caution.

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Find the t- test for the standard deviation of the two standard deviation numbers. 1. 0.75 2. 1.37

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