What is a confidence interval for a population mean? How does it change when you increase the sample size? How does it change when you raise the level of confidence? Are these corresponding changes to the confidence interval intuitive?
A confidence interval for the mean is a way of estimating the true population mean. Instead of a single number for themean, a confidence interval gives you a lower estimate and an upper estimate.
Formula for confidence interval is
Xbar +- z* (sigma/ √n)
Increasing sample size will decrease the width of the confidence interval .
When we raise the confidence level the width of the confidence interval increases and we confident that the true value will lie in the interval.
No, the are totally based on the formula but not intuitive . Logically if we see all of this makes sense . Because increasing the confidence level must increase the width so that we can be more confident and likewise its with the sample size.
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