# (a) Suppose the confidence level is .95 or 95. When we say that.pdf

9 de Apr de 2023
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### (a) Suppose the confidence level is .95 or 95. When we say that.pdf

• 1. (a) Suppose the confidence level is .95 or 95%. When we say that we are 95% confident that the population mean mu is within our confidence interval, what we really mean is that in long run (ie if we made many, many confidence intervals), 95% of all possible confidence intervals will contain the unknown population mean mu. Whether the confidence interval that we calculate contains mu, we will never know. But, we do know that 95% of the time, the formula xbar +/- t x s/sqrt(n) will give us a good confidence interval (on that contains mu) 95% of the time. (b) Note: The question says "assumption". But, to construct a t-CI for mu, we must the following 3 assumptions: To use the t-distribution, we must assume that (1) our sample is randomly sampled, (2) the population standard deviation is unknown and (3) the response variable is normally distributed. ---------------- I hope this helped. If you have any questions, please ask them in the comment section. :) Solution (a) Suppose the confidence level is .95 or 95%. When we say that we are 95% confident that the population mean mu is within our confidence interval, what we really mean is that in long run (ie if we made many, many confidence intervals), 95% of all possible confidence intervals will contain the unknown population mean mu. Whether the confidence interval that we calculate contains mu, we will never know. But, we do know that 95% of the time, the formula xbar +/- t x s/sqrt(n) will give us a good confidence interval (on that contains mu) 95% of the time. (b)
• 2. Note: The question says "assumption". But, to construct a t-CI for mu, we must the following 3 assumptions: To use the t-distribution, we must assume that (1) our sample is randomly sampled, (2) the population standard deviation is unknown and (3) the response variable is normally distributed. ---------------- I hope this helped. If you have any questions, please ask them in the comment section. :)