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  • Okay, class, today's lesson is about statistical tools. Can anyone tell me about the various statistical tools?
  • I can name a few, sir!, T-Test, F-Test, Linear Correlation and Analysis of Variance.
  • Yes, indeed! Do you have any suggestions for tools to use if the variance is known?
  • The difference in means has a normal distribution when the population variances are known. The variance of the difference is calculated by summing the variances and dividing them by the sample sizes. The variance of the sampling distribution of the sample means, according to the central limit theorem, is the variance divided by the sample size, so we are adding the variance of each mean together.
  • Is there anyone who can tell me if the variation is unknown?
  • If the population variances are unknown, the difference in means has a Student t-distribution, so we'll use the T-test.
  • Now that you know the tools to be used, What do you think is the importance of using Central Limit theorem?
  • I'm afraid I'm at a loss for words, sir!
  • Okay, Luke, the normality assumption is critical in statistics for parametric hypothesis tests of the mean, such as the t-test. As a result, you may believe that these tests are invalid when the data is not normally distributed. However, if your sample size is large enough, the central limit theorem takes effect and produces sampling distributions that are close to normal. Because of this, you can use these hypothesis tests even if your data is not normally distributed, as long as your sample size is large enough.
  • Does this imply that as sample size increases, the sampling distribution of the mean approaches a normal distribution?
  • Yes, you are correct! To summarize, the t-test is commonly used when the test statistic would have a normal distribution if the value of a scaling term in the test statistic was known. Furthermore, a two-sample t-test for equal sample sizes and equal variances is only used when both sample sizes are equal and the two distributions have the same variance. A two-sample t-test for unequal sample sizes and equal variances is also used only when the two distributions have the same variance.
  • Thank you very much, Sir, for this lesson; we learned a lot!
  • LUKE PIERRE PASCUAHUMSS 11 - C
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