What happens if your sample size is under 30, and you cannot use the Central Limit Theorem to verify the shape assumption? In this instance, we cannot use the Normal Curve, so we must use a flatter distribution with a wider spread called the t-distribution. The data is more spread out because less data = more variability = greater spread.
Each t-value is different. Unlike the z-critical values, we don't have set values for 90%, 95%, and 99%. Therefore, we have to calculate the critical value based on the size of our sample.
To calculate a t* critical value, first draw the normal curve with your level of confidence in the middle. For instance, if I was using 95%, I would draw the curve and put 95% in the middle. Then, take whatever area is left over on the LOWER end of the curve only and add it to the middle. I would have 2.5% left over, so I would add it to 95% to get 97.5%. Then, on your TI-84, go to 2nd - distribution and go to #4: t-interval. Fill in your percentage, but put it as a decimal (.975) and put in your sample size. Hit calculate, and this gives you the t-critical value to use in your confidence interval formula!
The interpretation and calculation is the same for t-intervals. The only difference is that, under assumptions, we need to state that the sample size was not sufficiently large, so a t-distribution must be used.
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