Notoriousb3 said:So as the title says. How do you calculate the confidence interval that is not on the t-table. For example how do you calculate the confidence interval for 97%? Assume that it is a normal distribution, you are not given σ and that n<30. Is there a formula? Or should i look for a more specific t-table?:P
Notoriousb3 said:Sorry but I don't understand your response what is "inversecdf" and "studenttdistribution". Also what kind of calculator would I need to calculate the inverse of the cumulative t-distribution? I'm rolling on a ti-83 plus and this baby has yet to fail me. Just to be clear, I know how to calculate a confidence interval for the following 80%, 90%, 95%, 98% and 99%. But I would like to know how you would calculate the confidence interval that cannot be solved with the student t distribution. i.e 93%, 97% etc.
There are several methods for calculating a confidence interval without using a t-table. One common method is to use a statistical software program, such as SPSS or Excel, which have built-in functions for calculating confidence intervals. Another method is to use an online calculator, which can be found easily with a quick internet search. Additionally, some textbooks provide tables or equations for calculating confidence intervals without using a t-table.
Yes, you can use a z-table to calculate a confidence interval if the sample size is large enough (typically n > 30). This is because the central limit theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, making the use of a z-table valid.
The level of confidence refers to the probability that the true population mean falls within the calculated confidence interval. Common levels of confidence used are 90%, 95%, and 99%. The choice of level of confidence is based on the desired level of precision and the trade-off between precision and confidence. A higher level of confidence will result in a wider confidence interval, while a lower level of confidence will result in a narrower interval.
The formula for calculating a confidence interval is: CI = x̄ ± (z/t)(s/√n) where x̄ is the sample mean, z/t is the critical value from the z/t distribution, s is the sample standard deviation, and n is the sample size. The critical value used will depend on the level of confidence and the type of distribution being used (z or t).
Yes, it is possible to calculate a confidence interval without knowing the population standard deviation. In this case, the sample standard deviation (s) is used instead. However, this will result in a wider confidence interval, making it less precise. To mitigate this, a larger sample size can be used which will result in a more accurate estimate of the population standard deviation.