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lilyungn
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Hi, I need help understanding how do I use t-distribution to estimate the tα/2 . Also what is meant when it asks "verify your result with empirical rule"
The t-distribution is a statistical probability distribution that is used to estimate the population mean when the sample size is small and the population standard deviation is unknown. It is similar to the normal distribution, but takes into account the added uncertainty due to the smaller sample size.
The tα/2 value is the critical value associated with a specific confidence level and degrees of freedom. It can be found using a t-table or by using a statistical software. The formula for calculating it is tα/2 = t(1-α/2, df), where α is the level of significance and df is the degrees of freedom.
The degrees of freedom for a t-distribution is equal to the sample size minus one. For example, if you have a sample size of 20, then the degrees of freedom would be 19.
The t-distribution is used to estimate tα/2 in order to calculate confidence intervals and perform hypothesis testing. It takes into account the added uncertainty due to the small sample size, resulting in more accurate estimates of the population mean.
The tα/2 value represents the critical value at which a certain percentage of the t-distribution falls below it. For example, if you have a tα/2 value of 2.042 and a confidence level of 95%, then you can say that 95% of the t-distribution falls below 2.042. This value is used to determine the margin of error in confidence intervals and to make decisions in hypothesis testing.